(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 759183, 24249]*) (*NotebookOutlinePosition[ 783385, 25126]*) (* CellTagsIndexPosition[ 783341, 25122]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Visualizing Combinatorial Enumeration", "Title"], Cell[TextData[ "We can not only count the number of cases resulting from the application of \ combinatorial functions \[LongDash] we can visualize them as well."], "Subsubtitle"], Cell[CellGroupData[{ Cell["by Robert Dickau", "Section"], Cell[TextData[{ "Combinatorics is the study of counting things, typically the number of \ ways one can select or arrange objects taken from some finite collection, \ possibly given one or more constraints. One characteristic of many formulas \ derived in combinatorics is that the results quickly become quite large \ (hence the term \[OpenCurlyDoubleQuote]combinatorial explosion\ \[CloseCurlyDoubleQuote]); a common example that demonstrates one advantage \ of using ", StyleBox["Mathematica", FontSlant->"Italic"], " over a pocket calculator, abacus, heap of stones, etc., is computing an \ exact result for 100 factorial." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(100!\)\)], "Input"], Cell[BoxData[ \(933262154439441526816992388562667004907159682643816214685929638952175999\ 932299156089414639761565182862536979208272237582511852109168640000000000000000\ 00000000\)], "Output"] }, Open ]], Cell[TextData[{ "It can be somewhat illuminating, as well as satisfying, to ", StyleBox["see", FontSlant->"Italic"], " the situations that (at least the smaller, down-to-earth siblings of) \ these unimaginably large numbers describe; it's one thing to be told there \ are thousands of stars visible to the naked eye, and quite another to go \ outside at night and look up." }], "Text"], Cell[TextData[{ "The purpose of this article is to enumerate and visualize situations \ described by elementary combinatorial functions. Note that Steven Skiena's \ standard add-on package ", StyleBox["DiscreteMath`Combinatorica`", "Input"], " defines hundreds of functions related to combinatorics and graph theory; \ our purpose here is not just to count cases, but also to visualize them." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Permutations and the factorial function", "Section"], Cell[TextData[{ "One of the first combinatorial functions that a student learns is the \ factorial function, which describes the number of ways to arrange a \ collection of distinct objects. For example, the letters A, B, and C can be \ arranged, or ", StyleBox["permuted", FontSlant->"Italic"], ", in six ways\[LongDash]ABC, ACB, BAC, BCA, CAB, and CBA. The derivation \ of a formula for computing the number of permutations of ", StyleBox["n", FontSlant->"Italic"], " objects typically goes something like this: assuming there are ", StyleBox["n", FontSlant->"Italic"], " items and ", StyleBox["n", FontSlant->"Italic"], " slots, there are ", StyleBox["n", FontSlant->"Italic"], " choices of item for the first slot; ", Cell[BoxData[ \(TraditionalForm\`n - 1\)]], " choices of item for the second slot; ", Cell[BoxData[ \(TraditionalForm\`n - 2\)]], " choices for the third slot, and so forth; until there is only one item \ left, which must be placed in the last (", Cell[BoxData[ \(TraditionalForm\`n\^th\)]], ") slot. Using the \[OpenCurlyDoubleQuote]multiplication rule\ \[CloseCurlyDoubleQuote], we conclude that for a collection of ", StyleBox["n", FontSlant->"Italic"], " objects there are ", Cell[BoxData[ \(TraditionalForm \`n\[Times]\((n - 1)\)\[Times]\((n - 2) \)\[Times]\[CenterEllipsis]\[Times]1\)]], ", otherwise known as ", StyleBox["n", FontSlant->"Italic"], " factorial (and denoted ", Cell[BoxData[ \(TraditionalForm\`\(n!\)\)]], "), different permutations." }], "Text"], Cell[TextData[{ "Texts usually go on to enumerate (or leave as an exercise to enumerate) \ the ", Cell[BoxData[ \(TraditionalForm\`\(4!\)\[InvisibleSpace] = 24\)]], " permutations of a collection of four objects, after which the matter is \ rightly dropped." }], "Text"], Cell[TextData[{ StyleBox["Mathematica", FontSlant->"Italic"], " has a built-in function called ", StyleBox["Permutations", "Input"], " which enumerates all the permutations of a list of items. Here is the \ answer to the traditional homework problem." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Permutations[{A, B, C, D}]\)], "Input"], Cell[BoxData[ \({{A, B, C, D}, {A, B, D, C}, {A, C, B, D}, {A, C, D, B}, {A, D, B, C}, { A, D, C, B}, {B, A, C, D}, {B, A, D, C}, {B, C, A, D}, {B, C, D, A}, { B, D, A, C}, {B, D, C, A}, {C, A, B, D}, {C, A, D, B}, {C, B, A, D}, { C, B, D, A}, {C, D, A, B}, {C, D, B, A}, {D, A, B, C}, {D, A, C, B}, { D, B, A, C}, {D, B, C, A}, {D, C, A, B}, {D, C, B, A}}\)], "Output"] }, Open ]], Cell[TextData[{ "Of course, ", StyleBox["Mathematica", FontSlant->"Italic"], " allows us to list all the permutations of any number of objects. Here is \ an abbreviated list of the 5,040 permutations of the numbers 1 through 7." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Permutations[Range[7]] // Short\)], "Input"], Cell[BoxData[ TagBox[ \({{1, 2, 3, 4, 5, 6, 7}, {1, 2, 3, 4, 5, 7, 6}, \[LeftSkeleton]5037\[RightSkeleton], {7, 6, 5, 4, 3, 2, 1}}\), Short]], "Output"] }, Open ]], Cell["\<\ The trouble is, permutations of numbers all look pretty much alike, \ or at least are equally uninteresting to read. Our first goal is to find a \ better way to visualize permutations.\ \>", "Text"], Cell[TextData[{ "One possibility is to graphically connect elements that are transposed in \ a particular permutation. Suppose we decide to represent the ", StyleBox["n", FontSlant->"Italic"], " elements being permuted by a number of points along a line, and connect \ two transposed elements with a semicircular arc. Here is a function that \ accepts a list of two positions, and returns a graphics object representing \ an arc joining the points; the semicircle is centered between the two points, \ and has a radius of half the distance between the points." }], "Text"], Cell[BoxData[ \(Semicircle[{m_, n_}] := Circle[{\(1\/2\) \((m + n)\), 0}, 1\/2\ Abs[m - n], {0, \[Pi]}]\)], "Input"], Cell[TextData[{ "We know from ", StyleBox["Mathematica", FontSlant->"Italic"], " experience that circles and perpendicular lines look wrong using the \ default setting for the graphics option ", StyleBox["AspectRatio", "Input"], ", so we'll use the setting ", StyleBox["Automatic", "Input"], "." }], "Text"], Cell[BoxData[ \(\(SetOptions[Graphics, AspectRatio \[Rule] Automatic]; \)\)], "Input"], Cell["Here is our first arc.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[Graphics[Semicircle[{1, 2}]]]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .5 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.928571 0.952381 0.0119048 0.952381 [ [ 0 0 0 0 ] [ 1 .5 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .5 L 0 .5 L closepath clip newpath 0 g .5 Mabswid newpath .5 .0119 .47619 0 180 arc s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{112.063, 56}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg1000`40O003h00OL7oo001`Ool000=o o`03001oogoo06Eoo`03001oogoo009oo`000goo00<007ooOol0IGoo00<007ooOol00Woo0003Ool0 0`00Oomoo`1UOol00`00Oomoo`02Ool000=oo`03001oogoo06Eoo`03001oogoo009oo`000goo00<0 07ooOol0IGoo00<007ooOol00Woo0003Ool00`00Oomoo`1UOol00`00Oomoo`02Ool000=oo`03001o ogoo06Eoo`03001oogoo009oo`000goo00<007ooOol0IGoo00<007ooOol00Woo0003Ool00`00Oomo o`1UOol00`00Oomoo`02Ool000Aoo`03001oogoo06=oo`03001oogoo00=oo`0017oo00<007ooOol0 Hgoo00<007ooOol00goo0004Ool00`00Oomoo`1SOol00`00Oomoo`03Ool000Aoo`03001oogoo06=o o`03001oogoo00=oo`0017oo00<007ooOol0Hgoo00<007ooOol00goo0005Ool00`00Oomoo`1QOol0 0`00Oomoo`04Ool000Eoo`03001oogoo065oo`03001oogoo00Aoo`001Woo00<007ooOol0Ggoo00<0 07ooOol01Goo0006Ool00`00Oomoo`1OOol00`00Oomoo`05Ool000Ioo`03001oogoo05moo`03001o ogoo00Eoo`001goo00<007ooOol0GGoo00<007ooOol01Woo0007Ool00`00Oomoo`1MOol00`00Oomo o`06Ool000Qoo`03001oogoo05]oo`03001oogoo00Moo`0027oo00<007ooOol0Fgoo00<007ooOol0 1goo0009Ool00`00Oomoo`1IOol00`00Oomoo`08Ool000Uoo`03001oogoo05Uoo`03001oogoo00Qo o`002Goo00<007ooOol0FGoo00<007ooOol027oo000:Ool00`00Oomoo`1GOol00`00Oomoo`09Ool0 00Yoo`03001oogoo05Moo`03001oogoo00Uoo`002goo00<007ooOol0EGoo00<007ooOol02Woo000; Ool00`00Oomoo`1EOol00`00Oomoo`0:Ool000aoo`03001oogoo05=oo`03001oogoo00]oo`003Goo 00<007ooOol0DGoo00<007ooOol037oo000>Ool00`00Oomoo`1?Ool00`00Oomoo`0=Ool000moo`03 001oogoo04ioo`03001oogoo00eoo`0047oo00<007ooOol0C7oo00<007ooOol03Woo000@Ool00`00 Oomoo`1;Ool00`00Oomoo`0?Ool0015oo`03001oogoo04Uoo`03001oogoo011oo`004Woo00<007oo Ool0Agoo00<007ooOol04Goo000COol00`00Oomoo`15Ool00`00Oomoo`0BOol001Aoo`03001oogoo 04=oo`03001oogoo01=oo`005Goo0P00@Goo0P005Woo000GOol00`00Oomoo`0mOol00`00Oomoo`0F Ool001Qoo`03001oogoo03]oo`03001oogoo01Moo`006Goo0P00>Goo0P006Woo000KOol00`00Oomo o`0eOol00`00Oomoo`0JOol001aoo`03001oogoo03=oo`03001oogoo01]oo`007Goo0`00;goo0`00 7Woo000POol2000[Ool2000QOol0029oo`8002Moo`8002=oo`0097oo0`008Goo0`009Goo000WOol2 000MOol2000XOol002Uoo`D001=oo`D002Yoo`00;Woo4`00;goo001`Ool00001\ \>"], ImageRangeCache->{{{0, 111.063}, {55, 0}} -> {0.969923, -0.0125027, 0.00954555, 0.00954555}}] }, Open ]], Cell[TextData[{ "We would now like to draw an arc connecting adjacent values in a given \ permutation. Let's first consider the identity permutation for the list ", Cell[BoxData[ \(TraditionalForm\`{1, 2, 3, 4}\)]], ". We can generate a list of adjacent pairs using ", StyleBox["Partition", "Input"], ", giving as a third argument the overlap between successive partitions." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Partition[{1, 2, 3, 4}, 2, 1]\)], "Input"], Cell[BoxData[ \({{1, 2}, {2, 3}, {3, 4}}\)], "Output"] }, Open ]], Cell[TextData[{ "We can then map our function ", StyleBox["Semicircle", "Input"], " over the partitioned list, and display the result." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[Graphics[Map[Semicircle, %]]]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .16667 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.00396825 0.31746 [ [ 0 0 0 0 ] [ 1 .16667 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .16667 L 0 .16667 L closepath clip newpath 0 g .5 Mabswid newpath .18254 .00397 .15873 0 180 arc s newpath .5 .00397 .15873 0 180 arc s newpath .81746 .00397 .15873 0 180 arc s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{246.5, 41.0625}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol00`00Oomoo`0mOol00`00Oomoo`0:Ool00`00Oomoo`0lOol00`00Oomoo`0:Ool00`00 Oomoo`0lOol00`00Oomoo`0=Ool000ioo`03001oogoo03eoo`03001oogoo00Yoo`03001oogoo03ao o`03001oogoo00Yoo`03001oogoo03aoo`03001oogoo00eoo`003goo00<007ooOol0>goo00<007oo Ool037oo00<007ooOol0>Woo00<007ooOol037oo00<007ooOol0>Woo00<007ooOol03Woo000?Ool0 0`00Oomoo`0jOol00`00Oomoo`0=Ool00`00Oomoo`0jOol00`00Oomoo`0Ool0011oo`03001oogoo03Qoo`03001oogoo00moo`03001oogoo03Qoo`03001oogoo 00ioo`03001oogoo03Qoo`03001oogoo00moo`004Goo0P00=goo00<007ooOol04Goo00<007ooOol0 =Goo0P004Woo0P00=goo00<007ooOol047oo000COol00`00Oomoo`0cOol00`00Oomoo`0COol00`00 Oomoo`0cOol00`00Oomoo`0DOol00`00Oomoo`0cOol00`00Oomoo`0AOol001Aoo`03001oogoo035o o`03001oogoo01Eoo`03001oogoo035oo`03001oogoo01Ioo`03001oogoo035oo`03001oogoo019o o`005Goo00<007ooOol0;goo00<007ooOol05goo00<007ooOol0;goo00<007ooOol05goo00<007oo Ool0<7oo00<007ooOol04goo000FOol00`00Oomoo`0]Ool00`00Oomoo`0IOol00`00Oomoo`0]Ool0 0`00Oomoo`0IOol00`00Oomoo`0^Ool00`00Oomoo`0DOol001Moo`8002]oo`8001eoo`8002]oo`80 01eoo`8002aoo`8001Moo`006Goo00<007ooOol09goo00<007ooOol07goo00<007ooOol09goo00<0 07ooOol07goo00<007ooOol0:7oo00<007ooOol05goo000JOol00`00Oomoo`0UOol00`00Oomoo`0Q Ool2000VOol00`00Oomoo`0QOol2000VOol2000JOol001]oo`8002=oo`8002Ioo`03001oogoo025o o`8002Ioo`8002=oo`03001oogoo01Yoo`007Goo0P007goo0P00:Goo0P0087oo00<007ooOol0:7oo 00<007ooOol07Woo0P007Goo000OOol3000IOol3000]Ool3000IOol4000/Ool4000HOol4000OOol0 029oo`@0015oo`@003=oo`@0019oo`<003Aoo`<0019oo`<002=oo`009Woo1`000goo1`00>goo1`00 0goo2000>Woo20000Woo20009Woo000]Ool30019Ool3001:Ool2000^Ool00001\ \>"], ImageRangeCache->{{{0, 245.5}, {40.0625, 0}} -> {0.891389, -0.0125, 0.0131048, 0.0131048}}] }, Open ]], Cell["\<\ Similarly, we can display a figure for an arbitrary permutation of \ a list.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[Graphics[Map[Semicircle, Partition[{1, 3, 4, 2}, 2, 1]]]]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .33333 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.00793651 0.31746 [ [ 0 0 0 0 ] [ 1 .33333 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .33333 L 0 .33333 L closepath clip newpath 0 g .5 Mabswid newpath .34127 .00794 .31746 0 180 arc s newpath .81746 .00794 .15873 0 180 arc s newpath .65873 .00794 .31746 0 180 arc s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{246.5, 82.0625}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol00`00Oomoo`1:Ool0 0`00Oomoo`0kOol00`00Oomoo`0GOol2000VOol2000:Ool00`00Oomoo`0Woo00<007ooOol06Woo0P0087oo0P0037oo00<0 07ooOol03Goo000@Ool00`00Oomoo`1:Ool00`00Oomoo`0hOol00`00Oomoo`0MOol2000LOol2000= Ool00`00Oomoo`0>Ool0011oo`03001oogoo04Yoo`03001oogoo03Qoo`03001oogoo01moo`<001Io o`<000moo`03001oogoo00ioo`0047oo00<007ooOol0Bgoo00<007ooOol0=Woo00<007ooOol08goo 10003Woo10004Goo00<007ooOol03goo000AOol00`00Oomoo`1;Ool00`00Oomoo`0dOol00`00Oomo o`0XOol>000DOol00`00Oomoo`0@Ool0015oo`03001oogoo04]oo`03001oogoo03Aoo`03001oogoo 04Yoo`03001oogoo011oo`004Woo00<007ooOol0Bgoo00<007ooOol0"], ImageRangeCache->{{{0, 245.5}, {81.0625, 0}} -> {0.910025, -0.0250053, 0.012953, 0.012953}}] }, Open ]], Cell[TextData[{ "One shortcoming of this way of visualizing permutations is that some \ different permutations have identical diagrams. Here is the diagram \ corresponding to ", Cell[BoxData[ \(TraditionalForm\`{4, 3, 2, 1}\)]], ", which is a permutation of ", Cell[BoxData[ \(TraditionalForm\`{1, 2, 3, 4}\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[Graphics[Map[Semicircle, Partition[{4, 3, 2, 1}, 2, 1]]]]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .16667 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.00396825 0.31746 [ [ 0 0 0 0 ] [ 1 .16667 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .16667 L 0 .16667 L closepath clip newpath 0 g .5 Mabswid newpath .81746 .00397 .15873 0 180 arc s newpath .5 .00397 .15873 0 180 arc s newpath .18254 .00397 .15873 0 180 arc s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{246.5, 41.0625}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol00`00Oomoo`0mOol00`00Oomoo`0:Ool00`00Oomoo`0lOol00`00Oomoo`0:Ool00`00 Oomoo`0lOol00`00Oomoo`0=Ool000ioo`03001oogoo03eoo`03001oogoo00Yoo`03001oogoo03ao o`03001oogoo00Yoo`03001oogoo03aoo`03001oogoo00eoo`003goo00<007ooOol0>goo00<007oo Ool037oo00<007ooOol0>Woo00<007ooOol037oo00<007ooOol0>Woo00<007ooOol03Woo000?Ool0 0`00Oomoo`0jOol00`00Oomoo`0=Ool00`00Oomoo`0jOol00`00Oomoo`0Ool0011oo`03001oogoo03Qoo`03001oogoo00moo`03001oogoo03Qoo`03001oogoo 00ioo`03001oogoo03Qoo`03001oogoo00moo`004Goo0P00=goo00<007ooOol04Goo00<007ooOol0 =Goo0P004Woo0P00=goo00<007ooOol047oo000COol00`00Oomoo`0cOol00`00Oomoo`0COol00`00 Oomoo`0cOol00`00Oomoo`0DOol00`00Oomoo`0cOol00`00Oomoo`0AOol001Aoo`03001oogoo035o o`03001oogoo01Eoo`03001oogoo035oo`03001oogoo01Ioo`03001oogoo035oo`03001oogoo019o o`005Goo00<007ooOol0;goo00<007ooOol05goo00<007ooOol0;goo00<007ooOol05goo00<007oo Ool0<7oo00<007ooOol04goo000FOol00`00Oomoo`0]Ool00`00Oomoo`0IOol00`00Oomoo`0]Ool0 0`00Oomoo`0IOol00`00Oomoo`0^Ool00`00Oomoo`0DOol001Moo`8002]oo`8001eoo`8002]oo`80 01eoo`8002aoo`8001Moo`006Goo00<007ooOol09goo00<007ooOol07goo00<007ooOol09goo00<0 07ooOol07goo00<007ooOol0:7oo00<007ooOol05goo000JOol00`00Oomoo`0UOol00`00Oomoo`0Q Ool2000VOol00`00Oomoo`0QOol2000VOol2000JOol001]oo`8002=oo`8002Ioo`03001oogoo025o o`8002Ioo`8002=oo`03001oogoo01Yoo`007Goo0P007goo0P00:Goo0P0087oo00<007ooOol0:7oo 00<007ooOol07Woo0P007Goo000OOol3000IOol3000]Ool3000IOol4000/Ool4000HOol4000OOol0 029oo`@0015oo`@003=oo`@0019oo`<003Aoo`<0019oo`<002=oo`009Woo1`000goo1`00>goo1`00 0goo2000>Woo20000Woo20009Woo000]Ool30019Ool3001:Ool2000^Ool00001\ \>"], ImageRangeCache->{{{0, 245.5}, {40.0625, 0}} -> {0.891389, -0.0125, 0.0131048, 0.0131048}}] }, Open ]], Cell[TextData[{ "The diagram for ", Cell[BoxData[ \(TraditionalForm\`{4, 3, 2, 1}\)]], " looks suspiciously similar to the diagram for ", Cell[BoxData[ \(TraditionalForm\`{1, 2, 3, 4}\)]], ". One way to distinguish between the two is to use different colors for \ the arcs in a diagram, in order to indicate which pair of adjacent elements \ is being displayed." }], "Text"], Cell["Here is a list of arcs.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(arcs = Map[Semicircle, Partition[{1, 2, 3, 4}, 2, 1]]\)], "Input"], Cell[BoxData[ \({Circle[{3\/2, 0}, 1\/2, {0, \[Pi]}], Circle[{5\/2, 0}, 1\/2, {0, \[Pi]}], Circle[{7\/2, 0}, 1\/2, {0, \[Pi]}]}\)], "Output"] }, Open ]], Cell[TextData[{ StyleBox["MapIndexed", "Input"], " lets us associate a gray level with each arc as a function of its \ position. Because ", StyleBox["GrayLevel", "Input"], " expects a value between 0 and 1, we divide the position of each arc by \ the number of elements in the list being permuted. (Of course there are only \ ", Cell[BoxData[ \(TraditionalForm\`n - 1\)]], " arcs involved in a list of ", StyleBox["n", FontSlant->"Italic"], " elements, but dividing by ", StyleBox["n", FontSlant->"Italic"], " keeps us from generating ", StyleBox["GrayLevel[1]", "Input"], ", or white, arcs, which don't show up against the default white \ background.)" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(MapIndexed[{GrayLevel[First[#2]/4], #}&, arcs]\)], "Input"], Cell[BoxData[ \({{GrayLevel[1\/4], Circle[{3\/2, 0}, 1\/2, {0, \[Pi]}]}, { GrayLevel[1\/2], Circle[{5\/2, 0}, 1\/2, {0, \[Pi]}]}, { GrayLevel[3\/4], Circle[{7\/2, 0}, 1\/2, {0, \[Pi]}]}}\)], "Output"] }, Open ]], Cell[TextData[{ "Here is our new diagram corresponding to ", Cell[BoxData[ \(TraditionalForm\`{1, 2, 3, 4}\)]], ", where the darkest arc connects the elements 1 and 2, the next-darkest \ arc connects 2 and\[NonBreakingSpace]3, and so forth." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[Graphics[%]]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .16667 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.00396825 0.31746 [ [ 0 0 0 0 ] [ 1 .16667 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .16667 L 0 .16667 L closepath clip newpath .25 g .5 Mabswid newpath .18254 .00397 .15873 0 180 arc s .5 g newpath .5 .00397 .15873 0 180 arc s .75 g newpath .81746 .00397 .15873 0 180 arc s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{246.5, 41.0625}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgMoogoo04Uo o`03?Nmoogoo04Uoo`03G_Moogoo04Yoo`03G_Moogoo00Ioo`0027oo00Moogoo04Uoo`03?Nmoogoo04Uoo`03?NmNmgoo 04Yoo`03G_Moogoo00Ioo`0027oo00Moogoo04Moo`037>Moocg_04Yoo`03?NmNmgoo04Uoo`03G_Moogoo00Moo`002Goo 00Moogoo049oo`037>Moogoo00Eoo`03?Nmo ogoo049oo`03?Nmoogoo00Aoo`03G_Moogoo049oo`03G_Moogoo00Yoo`002goo00Moogoo03moo`037>Moogoo00Qoo`03?Nmoogoo03ioo`03 ?Nmoogoo00Qoo`03G_Moogoo03ioo`03G_Moogoo00aoo`003Goo00Ool00acW Oomoo`0mOol00acWOomoo`0:Ool00cg_Oomoo`0lOol00cg_Oomoo`0:Ool00ekgOomoo`0lOol00ekg Oomoo`0=Ool000ioo`037>Moogoo03eoo`037>Moogoo00Yoo`03?Nmoogoo03aoo`03?Nmoogoo00Yo o`03G_Moogoo03aoo`03G_Moogoo00eoo`003goo00goo00Woo00Woo00=NmgooOol03Woo000?Ool00acWOomoo`0jOol0 0acWOomoo`0=Ool00cg_Oomoo`0jOol00cg_Oomoo`0Ool0 011oo`037>Moogoo03Qoo`037>Moogoo00moo`03?Nmoogoo03Qoo`03?Nmoogoo00ioo`03G_Moogoo 03Qoo`03G_Moogoo00moo`004Goo0QcW=goo00Moogoo035oo`037>Moogoo01Eo o`03?Nmoogoo035oo`03?Nmoogoo01Ioo`03G_Moogoo035oo`03G_Moogoo019oo`005Goo00LIOol37>L]Ool3?NlIOol4?Nl/Ool4G_LHOol4G_LOOol0029oo`@Lia5oo`@L ic=oo`@mka9oo`goo1cg_0goo23g_>Woo25kg 0Woo25kg9Woo000]Ool37>M9Ool3?Nm:Ool2G_L^Ool00001\ \>"], ImageRangeCache->{{{0, 245.5}, {40.0625, 0}} -> {0.891389, -0.0125, 0.0131048, 0.0131048}}] }, Open ]], Cell[TextData[{ "And here is the diagram for ", Cell[BoxData[ \(TraditionalForm\`{4, 3, 2, 1}\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(arcs = Map[Semicircle, Partition[{4, 3, 2, 1}, 2, 1]]; \n Show[Graphics[MapIndexed[{GrayLevel[First[#2]/4], #}&, arcs]]]; \)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .16667 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.00396825 0.31746 [ [ 0 0 0 0 ] [ 1 .16667 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .16667 L 0 .16667 L closepath clip newpath .25 g .5 Mabswid newpath .81746 .00397 .15873 0 180 arc s .5 g newpath .5 .00397 .15873 0 180 arc s .75 g newpath .18254 .00397 .15873 0 180 arc s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{246.5, 41.0625}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgMoogoo00Ioo`0027oo00=NmgooOol0BGoo00=Nmgoo Ool0BGoo00Moo`1:Ool00acWOomoo`06Ool000Qoo`03G_Moogoo04Uoo`03G_Moogoo04Uoo`03?NlLigoo 04Yoo`037>Moogoo00Ioo`0027oo00=NmgooOol0BGoo00=Nmcg_Ool0BGoo00Moo`19Ool00acWOomoo`07 Ool000Uoo`03G_Moogoo04Moo`03G_Moocg_04Yoo`03?NlLigoo04Uoo`037>Moogoo00Moo`002Goo 00=NmgooOol0Agoo00=Nmgoo?Nl0BWoo00Moogoo00Qoo`002Woo00=NmgooOol0AGoo00ENmgooOomo ocg_04Moo`03?Nmoogoo009oo`037>Moogoo04Aoo`037>Moogoo00Uoo`002Woo00=NmgooOol0AGoo 00ENmgooOomoocg_04Moo`03?Nmoogoo009oo`037>Moogoo04Aoo`037>Moogoo00Uoo`002goo00=N mgooOol0@goo00=NmgooOol00goo00Moogoo049oo`037>Moogoo00Yoo`002goo00=NmgooOol0@Woo 00=NmgooOol01Goo00Moogoo03ioo`037>Moogoo00aoo`003Goo00=NmgooOol0?goo00=NmgooOol0 27oo00Ool00ekg Oomoo`0mOol00ekgOomoo`0:Ool00cg_Oomoo`0lOol00cg_Oomoo`0:Ool00acWOomoo`0lOol00acW Oomoo`0=Ool000ioo`03G_Moogoo03eoo`03G_Moogoo00Yoo`03?Nmoogoo03aoo`03?Nmoogoo00Yo o`037>Moogoo03aoo`037>Moogoo00eoo`003goo00=NmgooOol0>goo00=NmgooOol037oo00Woo00Woo00Ool0 011oo`03G_Moogoo03Qoo`03G_Moogoo00moo`03?Nmoogoo03Qoo`03?Nmoogoo00ioo`037>Moogoo 03Qoo`037>Moogoo00moo`004Goo0Ukg=goo00=NmgooOol04Goo00Moogoo035oo`037>Moogoo019oo`005Goo00=Nmgoo Ool0;goo00=NmgooOol05goo00LVOol27>LJOol001]oo`9Nmb=oo`9NmbIoo`03?Nmoogoo025oo`8mkbIoo`8Lib=o o`037>Moogoo01Yoo`007Goo0Ukg7goo0Ukg:Goo0Sg_87oo00LHOol47>LOOol0029oo`ANma5oo`AN mc=oo`@mka9oo`goo1cg_0goo23g_>Woo21cW 0Woo21cW9Woo000]Ool3G_M9Ool3?Nm:Ool27>L^Ool00001\ \>"], ImageRangeCache->{{{0, 245.5}, {40.0625, 0}} -> {0.891389, -0.0125, 0.0131048, 0.0131048}}] }, Open ]], Cell[TextData[{ "(Note that this technique doesn't distinguish the permutations ", Cell[BoxData[ \(TraditionalForm\`{1, 2}\)]], " and ", Cell[BoxData[ \(TraditionalForm\`{2, 1}\)]], ", a complication that we'll just have to try to live with.)" }], "Text"], Cell[TextData[{ "A further improvement is to put all the diagrams corresponding to a list \ of permutations into an array. Since there are ", Cell[BoxData[ \(TraditionalForm\`\(n!\)\)]], " diagrams in each array, and ", Cell[BoxData[ \(TraditionalForm\`\(n!\)\)]], " is divisible by ", StyleBox["n", FontSlant->"Italic"], ", we can partition the complete list of permutations into rows of ", StyleBox["n", FontSlant->"Italic"], " elements. Actually, to keep the arrays from being too tall (as opposed to \ too wide), we'll partition each complete list into rows of ", Cell[BoxData[ \(TraditionalForm\`2 n\)]], " elements, which is safe because ", Cell[BoxData[ \(TraditionalForm\`\(n!\)\)]], " is divisible by ", Cell[BoxData[ \(TraditionalForm\`2 n\)]], ", provided ", StyleBox["n", FontSlant->"Italic"], " is greater than 2." }], "Text"], Cell["Here we put everything together into one function.", "Text"], Cell[BoxData[ \(ShowPermutationDiagrams[n_Integer /; n > 2] := \n\t With[{allpairs = Map[Partition[#, 2, 1]&, Permutations[Range[n]]]}, \(Show@\(GraphicsArray@Partition[#, 2 n]\)&\)@ Map[Graphics[#, PlotRange \[Rule] {Automatic, {\(-0.1\), n/2 + 0.1}}]&, Map[MapIndexed[{GrayLevel[First[#2]/n], #}&, #]&, Map[Semicircle, allpairs, {2}]]]]\)], "Input"], Cell["\<\ Here are the diagrams for permutations of lists containing 3, 4, \ and 5 elements.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(ShowPermutationDiagrams[3]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .12454 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.15873 0.00296529 0.15873 [ [ 0 0 0 0 ] [ 1 .12454 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .12454 L 0 .12454 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.00296529 0.17033 0.121577 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.452381 0.47619 0.047619 0.47619 [ [ 0 0 0 0 ] [ 1 .80952 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .80952 L 0 .80952 L closepath clip newpath .333 g .5 Mabswid newpath .2619 .04762 .2381 0 180 arc s .667 g newpath .7381 .04762 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.184982 0.00296529 0.331502 0.121577 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.452381 0.47619 0.047619 0.47619 [ [ 0 0 0 0 ] [ 1 .80952 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .80952 L 0 .80952 L closepath clip newpath .333 g .5 Mabswid newpath .5 .04762 .47619 0 180 arc s .667 g newpath .7381 .04762 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.346154 0.00296529 0.492674 0.121577 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.452381 0.47619 0.047619 0.47619 [ [ 0 0 0 0 ] [ 1 .80952 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .80952 L 0 .80952 L closepath clip newpath .333 g .5 Mabswid newpath .2619 .04762 .2381 0 180 arc s .667 g newpath .5 .04762 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.507326 0.00296529 0.653846 0.121577 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.452381 0.47619 0.047619 0.47619 [ [ 0 0 0 0 ] [ 1 .80952 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .80952 L 0 .80952 L closepath clip newpath .333 g .5 Mabswid newpath .7381 .04762 .2381 0 180 arc s .667 g newpath .5 .04762 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.668498 0.00296529 0.815018 0.121577 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.452381 0.47619 0.047619 0.47619 [ [ 0 0 0 0 ] [ 1 .80952 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .80952 L 0 .80952 L closepath clip newpath .333 g .5 Mabswid newpath .5 .04762 .47619 0 180 arc s .667 g newpath .2619 .04762 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.82967 0.00296529 0.97619 0.121577 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.452381 0.47619 0.047619 0.47619 [ [ 0 0 0 0 ] [ 1 .80952 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .80952 L 0 .80952 L closepath clip newpath .333 g .5 Mabswid newpath .7381 .04762 .2381 0 180 arc s .667 g newpath .2619 .04762 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{287.438, 35.75}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol012U:Oomooe:d3goo00=B]7ooOol01Woo00goo000mOol00bU:Oomoo`0I Ool00bU:Oomoo`0>Ool00e:dOomoo`0IOol00e:dOomoo`0>Ool00e:dOomoo`0IOol00e:dOomoo`0> Ool00bU:Oomoo`0IOol00bU:Oomoo`0lOol003ioo`03:DYoogoo01Moo`03:DYoogoo011oo`03D[Ao ogoo01Moo`03D[Aoogoo011oo`03D[Aoogoo01Moo`03D[Aoogoo011oo`03:DYoogoo01Moo`03:DYo ogoo03eoo`00?goo00"], ImageRangeCache->{{{0, 286.438}, {34.75, 0}} -> {-0.233661, -0.0186813, 0.0225785, 0.0225785}, {{10.3125, 51.1875}, {33.875, 0.8125}} -> { 0.418912, -0.14499, 0.0514176, 0.0514176}, {{55.3125, 96.1875}, {33.875, 0.8125}} -> {-1.89488, -0.14499, 0.0514176, 0.0514176}, {{100.25, 141.125}, {33.875, 0.8125}} -> {-4.20546, -0.14499, 0.0514176, 0.0514176}, {{145.25, 186.125}, {33.875, 0.8125}} -> {-6.51925, -0.14499, 0.0514176, 0.0514176}, {{190.188, 231.063}, {33.875, 0.8125}} -> {-8.82983, -0.14499, 0.0514176, 0.0514176}, {{235.188, 276.063}, {33.875, 0.8125}} -> {-11.1436, -0.14499, 0.0514176, 0.0514176}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(ShowPermutationDiagrams[4]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .25689 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.119048 0.00611637 0.119048 [ [ 0 0 0 0 ] [ 1 .25689 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .25689 L 0 .25689 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.00611637 0.133279 0.082571 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .81746 .03175 .15873 0 180 arc s .5 g newpath .5 .03175 .47619 0 180 arc s .75 g newpath .18254 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.144226 0.00611637 0.253695 0.082571 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .81746 .03175 .15873 0 180 arc s .5 g newpath .65873 .03175 .31746 0 180 arc s .75 g newpath .18254 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.264641 0.00611637 0.374111 0.082571 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .5 .03175 .47619 0 180 arc s .5 g newpath .18254 .03175 .15873 0 180 arc s .75 g newpath .5 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.385057 0.00611637 0.494527 0.082571 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .5 .03175 .47619 0 180 arc s .5 g newpath .34127 .03175 .31746 0 180 arc s .75 g newpath .5 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.505473 0.00611637 0.614943 0.082571 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .65873 .03175 .31746 0 180 arc s .5 g newpath .18254 .03175 .15873 0 180 arc s .75 g newpath .34127 .03175 .31746 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.625889 0.00611637 0.735359 0.082571 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .65873 .03175 .31746 0 180 arc s .5 g newpath .5 .03175 .15873 0 180 arc s .75 g newpath .34127 .03175 .31746 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.746305 0.00611637 0.855774 0.082571 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .81746 .03175 .15873 0 180 arc s .5 g newpath .34127 .03175 .31746 0 180 arc s .75 g newpath .18254 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.866721 0.00611637 0.97619 0.082571 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .81746 .03175 .15873 0 180 arc s .5 g newpath .5 .03175 .15873 0 180 arc s .75 g newpath .18254 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.0902164 0.133279 0.166671 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .5 .03175 .15873 0 180 arc s .5 g newpath .34127 .03175 .31746 0 180 arc s .75 g newpath .5 .03175 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.144226 0.0902164 0.253695 0.166671 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .5 .03175 .15873 0 180 arc s .5 g newpath .81746 .03175 .15873 0 180 arc s .75 g newpath .5 .03175 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.264641 0.0902164 0.374111 0.166671 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .65873 .03175 .31746 0 180 arc s .5 g newpath .5 .03175 .47619 0 180 arc s .75 g newpath .34127 .03175 .31746 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.385057 0.0902164 0.494527 0.166671 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .65873 .03175 .31746 0 180 arc s .5 g newpath .81746 .03175 .15873 0 180 arc s .75 g newpath .34127 .03175 .31746 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.505473 0.0902164 0.614943 0.166671 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .34127 .03175 .31746 0 180 arc s .5 g newpath .18254 .03175 .15873 0 180 arc s .75 g newpath .65873 .03175 .31746 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.625889 0.0902164 0.735359 0.166671 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .34127 .03175 .31746 0 180 arc s .5 g newpath .5 .03175 .47619 0 180 arc s .75 g newpath .65873 .03175 .31746 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.746305 0.0902164 0.855774 0.166671 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .5 .03175 .15873 0 180 arc s .5 g newpath .18254 .03175 .15873 0 180 arc s .75 g newpath .5 .03175 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.866721 0.0902164 0.97619 0.166671 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .5 .03175 .15873 0 180 arc s .5 g newpath .65873 .03175 .31746 0 180 arc s .75 g newpath .5 .03175 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.174316 0.133279 0.250771 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .18254 .03175 .15873 0 180 arc s .5 g newpath .5 .03175 .15873 0 180 arc s .75 g newpath .81746 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.144226 0.174316 0.253695 0.250771 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .18254 .03175 .15873 0 180 arc s .5 g newpath .65873 .03175 .31746 0 180 arc s .75 g newpath .81746 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.264641 0.174316 0.374111 0.250771 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .34127 .03175 .31746 0 180 arc s .5 g newpath .5 .03175 .15873 0 180 arc s .75 g newpath .65873 .03175 .31746 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.385057 0.174316 0.494527 0.250771 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .34127 .03175 .31746 0 180 arc s .5 g newpath .81746 .03175 .15873 0 180 arc s .75 g newpath .65873 .03175 .31746 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.505473 0.174316 0.614943 0.250771 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .5 .03175 .47619 0 180 arc s .5 g newpath .65873 .03175 .31746 0 180 arc s .75 g newpath .5 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.625889 0.174316 0.735359 0.250771 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .5 .03175 .47619 0 180 arc s .5 g newpath .81746 .03175 .15873 0 180 arc s .75 g newpath .5 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.746305 0.174316 0.855774 0.250771 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .18254 .03175 .15873 0 180 arc s .5 g newpath .34127 .03175 .31746 0 180 arc s .75 g newpath .81746 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.866721 0.174316 0.97619 0.250771 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .18254 .03175 .15873 0 180 arc s .5 g newpath .5 .03175 .47619 0 180 arc s .75 g newpath .81746 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{287.875, 73.9375}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgMoogoo00Moo`03?Nmoogoo009oo`03G_Mo ogoo00Ioo`03G_Moogoo00Moo`037>Moogoo00Moo`03?Nmoogoo009oo`03?Nmoogoo00Moo`03G_Mo ogoo00Moo`03G_Moogoo00Ioo`037>Moogoo009oo`03?Nmoogoo00Moo`03G_Moogoo00Moo`03G_Mo ogoo00Moo`057>MoogooOomNm`09Ool00cg_Oomoo`07Ool00ekgOomoo`07Ool01AcWOomoogooG_L0 2Goo00Moogoo009oo`03G_Moogoo00Ioo`037>Lmkgoo00Moo`03G_Moogoo00Moo`037>Moogoo009o o`03G_Moogoo00Ioo`03G_Moogoo00Moo`03?NlLigoo00Moo`037>Moogoo009oo`03G_Moogoo00Io o`03G_Lmkgoo00Moo`03?NlLigoo00Moo`037>Moogoo00Moo`002Goo00=NmgooOol01Woo00=Nmgoo Ool027oo00L01goo00=NmgooOol01goo 00L01Woo00L6Ool00acWOomoo`08Ool000Uoo`03?NmNmgoo00Eoo`03G_Mo ogoo00Yoo`037>Moogoo00Aoo`037>Lmkgoo00Aoo`03G_Moogoo00Aoo`03G_Moocg_00Yoo`037>Mo ogoo00Aoo`037>Lmkgoo00=oo`037>Lmkgoo00Eoo`04?NmoogooG_L6Ool00ekgOomoo`08Ool00acW Oomoo`02Ool00acW?Nmoo`08Ool00ekgOomoo`04Ool00ekg?Nmoo`08Ool00acWOomoo`03Ool00ekg ?Nmoo`05Ool00cg_OolLi`07Ool00ekgOomoo`07Ool00acWOomoo`03Ool00ekgOomoo`07Ool00acW ?Nmoo`05Ool00ekgOomoo`07Ool00acWOomoo`03Ool00cg_G_Moo`05Ool00ekgOomoo`08Ool00cg_ OolLi`06Ool00acWOomoo`04Ool00ekgOomoo`04Ool015kgOomoocg_1Woo00@mkgooOolLi`Ioo`03 7>Moogoo00Qoo`002Woo00Moogoo00Moo`03 ?Nmoogoo00]oo`8mkcMoo`002goo00L=Ool2G_L7Ool3G_L7Ool37>LMoogoo01Aoo`03 7>Moogoo00Qoo`047>MoogooOol7?NlLAOol7G_L3Ool77>LB Ool6?NllOol000eoo`03?Nmoogoo019oo`03?Nmoogoo02aoo`037>Moogoo019oo`037>Moogoo00Yo o`037>Moogoo019oo`037>Moogoo09Aoo`003Woo00Ool00cg_Oomoo`0aOol27>L>Ool2 7>LAOol00acWOomoo`0NHOol0015oo`8mk`Uoo`Moogoo00Moo`05G_MoogooOolmk`09Ool00ekgOomoo`07Ool00acWOomoo`07Ool00ekg Oomoo`02Ool00ekgOomoo`06Ool00cg_Oomoo`07Ool00acWOomoo`07Ool00ekgOomoo`02Ool00ekg Oomoo`07Ool00cg_Oomoo`07Ool00acWOomoo`06Ool00ekgOomoo`07Ool000Qoo`03G_Lmkgoo00Qo o`037>Moogoo00Ioo`03?Nmoogoo00Moo`03G_Moogoo009oo`03G_Moogoo00Moo`037>Moogoo00Io o`037>Lmkgoo00Moo`03G_Moogoo009oo`03G_Moogoo00Moo`037>Moogoo00Ioo`03G_Moogoo00Mo o`03?Nmoogoo009oo`03G_Moogoo00Moo`037>Moogoo00Moo`03G_Moogoo00Ioo`03?Nmoogoo009o o`037>Lmkgoo00Moo`03G_Moogoo00Moo`037>Moogoo00Moo`06G_MoogooOolmkacW27oo00=Nmgoo Ool01goo00Moo`07Ool00acWOomoo`07Ool00ekgOomoo`02Ool00ekgOomoo`07Ool0 0cg_Oomoo`06Ool00acWOomoo`07Ool00ekgOomoo`07Ool000Uoo`03G_Moogoo00Qoo`037>Moogoo 00Aoo`03?Nmoogoo00Qoo`03G_Moogoo009oo`03G_Moogoo00Qoo`037>Moogoo00Aoo`047>Moogoo ?Nl6Ool00cg_G_Moo`03Ool00cg_G_Moo`07Ool00acWOomoo`06Ool00ekgOomoo`07Ool00cg_Oomo o`03Ool00ekgOomoo`07Ool00acWOomoo`05Ool00ekgOolmk`06Ool00cg_7>Moo`04Ool00acW?Nmo o`05Ool00cg_OomNm`07Ool00acWOomoo`07Ool00ekgOomoo`03Ool00cg_Oomoo`07Ool00ekgOomo o`05Ool00acWOomoo`07Ool00ekg?Nmoo`03Ool00ekg?Nmoo`05Ool013g_OomooacW1Woo00Moogoo00Qoo`03G_Moogoo009oo`03G_Moogoo00Mo o`03?NlLigoo00Eoo`037>Moogoo00Qoo`03G_Moogoo00Moo`002Woo00=NmgooOol027oo1QcW00Moogoo00Eoo`037>Lmkcg_00@mk`=oo`03G_Moogoo00=oo`03 7>Moogoo00Moo`03G_Moogoo00Aoo`03?NlLigoo00Qoo`03G_Moogoo00=oo`037>Moogoo00Moo`03 G_Lmkgoo00Eoo`03G_Lmkcg_00@mk`Aoo`HLi`Yoo`03G_Moogoo00Aoo`03G_Moogoo00Moo`03?NlL iacW00@Li`Yoo`03G_Moogoo00Qoo`002Woo00=NmgooOol03Woo00L3Ool00ekgOomoo`07 Ool00cg_Oomoo`07Ool00ekgOomoo`07Ool01AcWOomoogooG_L02Goo00MNmekg00Qoo`8Li`03?Nmoogoo00Qoo`03G_Moogoo 00Moo`037>MNmekg00Qoo`8Li`]oo`8Li`Qoo`03G_MooacW00Qoo`9Nm`Yoo`03?NlLiacW00Qoo`9N m`037>Moogoo00Moo`03G_Moocg_00Qoo`03G_Moogoo01Ioo`03G_Moogoo00Ioo`03G_Moogoo00Uo o`03?Nmoogoo00Qoo`03?Nmooekg00]oo`0037oo00ANmgoo?Nlmk`Ioo`8mk`]oo`03G_Moogoo00Qo o`03G_Moogoo01Aoo`03G_Moogoo00Qoo`04?NmooekgG_L6Ool2G_L27>L6Ool27>L00goo?Nmoo`0; Ool2G_L7Ool00ekg7>LLi`07Ool00acWOomoo`0=Ool00acWOomoo`05Ool00acWG_MNm`07Ool00ekg Oomoo`0;Ool00cg_OolLi`07Ool27>L00ekgOomoo`05Ool2G_L00goo?Nmoo`09Ool00ekgOomoo`0D Ool00ekgOomoo`08Ool00ekgOomoo`09Ool2?Nl6Ool2?Nl00gooG_Moo`0;Ool000aoo`04G_Moogoo Ool6?Nl=Ool00ekgOomoo`08Ool00ekgOomoo`0DOol00ekgOomoo`08Ool013g_Oomoogoo1Ukg17oo 1QcW0goo00Moogoo00Moo`03?Nmoogoo00Moo`03G_Mo ogoo00Moo`03G_Moogoo009oo`037>Moogoo00Ioo`03?Nmoogoo00Moo`03G_Moogoo00Moo`03G_Mo ogoo009oo`037>Moogoo00Moo`03G_Moogoo00Moo`03?Nmoogoo00Ioo`03G_Moogoo009oo`037>Mo ogoo00Moo`03G_Moogoo00Moo`03?Nmoogoo00Moo`05G_MoogooOolLi`09Ool00ekgOomoo`07Ool0 0ekgOomoo`07Ool01Cg_Oomoogoo7>L02Goo00=NmgooOol01goo00=NmgooOol01goo00L02Woo00=NmgooOol01Woo 00=Nmcg_Ool01goo00Moogoo00Aoo`047>Moogoo?Nl6Ool0 13g_Oomooekg1Woo00=NmgooOol017oo00Moogoo00Qoo`03?Nmooekg00Io o`03G_Moogoo00=oo`03?NlLigoo00Eoo`037>Moogoo00Yoo`03G_Moogoo00Aoo`03G_Lmkgoo00Qo o`002Woo00Moo`08Ool00ekgOomoo`03Ool00acWOomoo`07Ool00ekgOomoo`05Ool00acW Oolmk`06Ool00cg_G_Moo`03Ool00acWOomoo`08Ool00cg_G_Moo`04Ool00ekgOomoo`08Ool00cg_ 7>Moo`03Ool00acWOomoo`08Ool00ekgOomoo`04Ool015kgOomoocg_1Woo00L4Ool6?Nl4Ool6G_L8Ool67>L3 Ool00cg_Oomoo`08Ool6G_L00cg_Oomoo`04Ool00acWOomoo`07Ool00ekg?Nlmk`04?Nl00acWOomo o`07Ool00ekgOomoo`05Ool00acWOomoo`07Ool00ekgOomoo`03Ool011cWOomoogoo1Sg_00=Nmgoo Ool017oo00L011cW2Woo00@mkgooOomoo`INm`Moo`03?NlLiacW00@L i`ioo`INm`03?Nmoogoo00Qoo`00=Woo00L8Ool2G_L3Ool00acWOomoo`07Ool0 0ekgOomoo`07Ool00acWOomoo`07Ool01EkgOomoogoo7>L02Goo00=NmgooOol01Woo00LLi`08Ool2G_L;Ool00acWOomoo`07Ool00ekg7>LLi`08Ool2G_L:Ool00acW Oomoo`08Ool00cg_Oomoo`08Ool2?Nl00acWOomoo`07Ool00acWOomoo`0FOol00acWOomoo`07Ool2 ?Nl:Ool00cg_Oomoo`0BOol00cg_Oomoo`0FOol00cg_Oomoo`09Ool003Yoo`8mk`Ioo`8mk`ioo`8L i`Ioo`8Li`9Nm`Ioo`9Nm`ioo`8Li`Moo`037>MNmekg00Moo`03G_Moogoo00]oo`037>Moogoo00Qo o`8mk`Moo`03?NmooacW00]oo`037>Moogoo01Aoo`037>Moogoo00Yoo`8mk`Ioo`8mkaIoo`03?Nmo ogoo01Aoo`03?Nmoogoo00Yoo`00?7oo1Sg_4Woo1QcW17oo1Ukg4Woo1acW0goo1ekg3Woo00L^Ool00cg_Oomoo`0BOol00cg_Oomoo`0;Ool009Moo`8Li`moo`8Li`moo`8Li`moo`8Lic5oo`8m ka1oo`8mk`ioo`00VGoo00L9Ool27>LFOol00acWOomoo`07Ool27>LhOol2?Nl8Ool2?NlBOol009ao o`TLiaUoo`TLicaoo`PmkaAoo`00ogoo87oo003oOolPOol00?moob1oo`00ogoo87oo003oOolPOol0 0?moob1oo`00ogoo87oo0000\ \>"], ImageRangeCache->{{{0, 286.875}, {72.9375, 0}} -> {-0.243637, -0.0513773, 0.0295852, 0.0295852}, {{8.1875, 39.3125}, {71.1875, 49.4375}} -> { 0.0963863, -0.277715, 0.101205, 0.101205}, {{42.375, 73.5}, {71.1875, 49.4375}} -> {-3.36356, -0.277715, 0.101205, 0.101205}, {{76.5625, 107.688}, {71.1875, 49.4375}} -> {-6.8235, -0.277715, 0.101205, 0.101205}, {{110.75, 141.875}, {71.1875, 49.4375}} -> {-10.2834, -0.277715, 0.101205, 0.101205}, {{144.938, 176.063}, {71.1875, 49.4375}} -> {-13.7434, -0.277715, 0.101205, 0.101205}, {{179.125, 210.25}, {71.1875, 49.4375}} -> {-17.2033, -0.277715, 0.101205, 0.101205}, {{213.313, 244.438}, {71.1875, 49.4375}} -> {-20.6633, -0.277715, 0.101205, 0.101205}, {{247.5, 278.625}, { 71.1875, 49.4375}} -> {-24.1232, -0.277715, 0.101205, 0.101205}, {{8.1875, 39.3125}, {47.3125, 25.5625}} -> {0.0963863, -2.69398, 0.101205, 0.101205}, {{42.375, 73.5}, {47.3125, 25.5625}} -> {-3.36356, -2.69398, 0.101205, 0.101205}, {{76.5625, 107.688}, {47.3125, 25.5625}} -> {-6.8235, -2.69398, 0.101205, 0.101205}, {{110.75, 141.875}, { 47.3125, 25.5625}} -> {-10.2834, -2.69398, 0.101205, 0.101205}, {{144.938, 176.063}, {47.3125, 25.5625}} -> {-13.7434, -2.69398, 0.101205, 0.101205}, {{179.125, 210.25}, {47.3125, 25.5625}} -> {-17.2033, -2.69398, 0.101205, 0.101205}, {{213.313, 244.438}, {47.3125, 25.5625}} -> {-20.6633, -2.69398, 0.101205, 0.101205}, {{247.5, 278.625}, { 47.3125, 25.5625}} -> {-24.1232, -2.69398, 0.101205, 0.101205}, {{8.1875, 39.3125}, {23.4375, 1.6875}} -> {0.0963863, -5.11025, 0.101205, 0.101205}, {{42.375, 73.5}, {23.4375, 1.6875}} -> {-3.36356, -5.11025, 0.101205, 0.101205}, {{76.5625, 107.688}, {23.4375, 1.6875}} -> {-6.8235, -5.11025, 0.101205, 0.101205}, {{110.75, 141.875}, { 23.4375, 1.6875}} -> {-10.2834, -5.11025, 0.101205, 0.101205}, {{144.938, 176.063}, {23.4375, 1.6875}} -> {-13.7434, -5.11025, 0.101205, 0.101205}, {{ 179.125, 210.25}, {23.4375, 1.6875}} -> {-17.2033, -5.11025, 0.101205, 0.101205}, {{213.313, 244.438}, {23.4375, 1.6875}} -> {-20.6633, -5.11025, 0.101205, 0.101205}, {{247.5, 278.625}, {23.4375, 1.6875}} -> {-24.1232, -5.11025, 0.101205, 0.101205}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(ShowPermutationDiagrams[5]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .77261 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0952381 0.0183954 0.0952381 [ [ 0 0 0 0 ] [ 1 .77261 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .77261 L 0 .77261 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.0183954 0.111184 0.0745647 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .7381 .02381 .2381 0 180 arc s .4 g newpath .38095 .02381 .11905 0 180 arc s .6 g newpath .14286 .02381 .11905 0 180 arc s .8 g newpath .38095 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.119921 0.0183954 0.207296 0.0745647 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .7381 .02381 .2381 0 180 arc s .4 g newpath .38095 .02381 .11905 0 180 arc s .6 g newpath .5 .02381 .2381 0 180 arc s .8 g newpath .38095 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.216033 0.0183954 0.303408 0.0745647 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .7381 .02381 .2381 0 180 arc s .4 g newpath .61905 .02381 .11905 0 180 arc s .6 g newpath .38095 .02381 .35714 0 180 arc s .8 g newpath .14286 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.312145 0.0183954 0.399519 0.0745647 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .7381 .02381 .2381 0 180 arc s .4 g newpath .61905 .02381 .11905 0 180 arc s .6 g newpath .5 .02381 .2381 0 180 arc s .8 g newpath .14286 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.408257 0.0183954 0.495631 0.0745647 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .85714 .02381 .11905 0 180 arc s .4 g newpath .38095 .02381 .35714 0 180 arc s .6 g newpath .14286 .02381 .11905 0 180 arc s .8 g newpath .38095 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.504369 0.0183954 0.591743 0.0745647 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .85714 .02381 .11905 0 180 arc s .4 g newpath .38095 .02381 .35714 0 180 arc s .6 g newpath .2619 .02381 .2381 0 180 arc s .8 g newpath .38095 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.600481 0.0183954 0.687855 0.0745647 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .85714 .02381 .11905 0 180 arc s .4 g newpath .5 .02381 .2381 0 180 arc s .6 g newpath .14286 .02381 .11905 0 180 arc s .8 g newpath .2619 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.696592 0.0183954 0.783967 0.0745647 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .85714 .02381 .11905 0 180 arc s .4 g newpath .5 .02381 .2381 0 180 arc s .6 g newpath .38095 .02381 .11905 0 180 arc s .8 g newpath .2619 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.792704 0.0183954 0.880079 0.0745647 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .85714 .02381 .11905 0 180 arc s .4 g newpath .61905 .02381 .11905 0 180 arc s .6 g newpath .2619 .02381 .2381 0 180 arc s .8 g newpath .14286 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.888816 0.0183954 0.97619 0.0745647 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .85714 .02381 .11905 0 180 arc s .4 g newpath .61905 .02381 .11905 0 180 arc s .6 g newpath .38095 .02381 .11905 0 180 arc s .8 g newpath .14286 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.0801816 0.111184 0.136351 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .47619 0 180 arc s .4 g newpath .38095 .02381 .35714 0 180 arc s .6 g newpath .5 .02381 .2381 0 180 arc s .8 g newpath .38095 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.119921 0.0801816 0.207296 0.136351 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .47619 0 180 arc s .4 g newpath .38095 .02381 .35714 0 180 arc s .6 g newpath .61905 .02381 .11905 0 180 arc s .8 g newpath .38095 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.216033 0.0801816 0.303408 0.136351 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .35714 0 180 arc s .4 g newpath .14286 .02381 .11905 0 180 arc s .6 g newpath .2619 .02381 .2381 0 180 arc s .8 g newpath .61905 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.312145 0.0801816 0.399519 0.136351 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .35714 0 180 arc s .4 g newpath .14286 .02381 .11905 0 180 arc s .6 g newpath .38095 .02381 .35714 0 180 arc s .8 g newpath .61905 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.408257 0.0801816 0.495631 0.136351 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .35714 0 180 arc s .4 g newpath .38095 .02381 .11905 0 180 arc s .6 g newpath .2619 .02381 .2381 0 180 arc s .8 g newpath .38095 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.504369 0.0801816 0.591743 0.136351 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .35714 0 180 arc s .4 g newpath .38095 .02381 .11905 0 180 arc s .6 g newpath .61905 .02381 .11905 0 180 arc s .8 g newpath .38095 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.600481 0.0801816 0.687855 0.136351 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .35714 0 180 arc s .4 g newpath .5 .02381 .2381 0 180 arc s .6 g newpath .38095 .02381 .35714 0 180 arc s .8 g newpath .2619 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.696592 0.0801816 0.783967 0.136351 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .35714 0 180 arc s .4 g newpath .5 .02381 .2381 0 180 arc s .6 g newpath .61905 .02381 .11905 0 180 arc s .8 g newpath .2619 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.792704 0.0801816 0.880079 0.136351 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .7381 .02381 .2381 0 180 arc s .4 g newpath .2619 .02381 .2381 0 180 arc s .6 g newpath .14286 .02381 .11905 0 180 arc s .8 g newpath .5 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.888816 0.0801816 0.97619 0.136351 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .7381 .02381 .2381 0 180 arc s .4 g newpath .2619 .02381 .2381 0 180 arc s .6 g newpath .38095 .02381 .35714 0 180 arc s .8 g newpath .5 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.141968 0.111184 0.198137 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .85714 .02381 .11905 0 180 arc s .4 g newpath .5 .02381 .47619 0 180 arc s .6 g newpath .14286 .02381 .11905 0 180 arc s .8 g newpath .38095 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.119921 0.141968 0.207296 0.198137 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .85714 .02381 .11905 0 180 arc s .4 g newpath .5 .02381 .47619 0 180 arc s .6 g newpath .2619 .02381 .2381 0 180 arc s .8 g newpath .38095 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.216033 0.141968 0.303408 0.198137 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .85714 .02381 .11905 0 180 arc s .4 g newpath .61905 .02381 .35714 0 180 arc s .6 g newpath .14286 .02381 .11905 0 180 arc s .8 g newpath .2619 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.312145 0.141968 0.399519 0.198137 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .85714 .02381 .11905 0 180 arc s .4 g newpath .61905 .02381 .35714 0 180 arc s .6 g newpath .38095 .02381 .11905 0 180 arc s .8 g newpath .2619 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.408257 0.141968 0.495631 0.198137 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .85714 .02381 .11905 0 180 arc s .4 g newpath .7381 .02381 .2381 0 180 arc s .6 g newpath .2619 .02381 .2381 0 180 arc s .8 g newpath .14286 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.504369 0.141968 0.591743 0.198137 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .85714 .02381 .11905 0 180 arc s .4 g newpath .7381 .02381 .2381 0 180 arc s .6 g newpath .38095 .02381 .11905 0 180 arc s .8 g newpath .14286 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.600481 0.141968 0.687855 0.198137 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .47619 0 180 arc s .4 g newpath .14286 .02381 .11905 0 180 arc s .6 g newpath .38095 .02381 .11905 0 180 arc s .8 g newpath .61905 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.696592 0.141968 0.783967 0.198137 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .47619 0 180 arc s .4 g newpath .14286 .02381 .11905 0 180 arc s .6 g newpath .5 .02381 .2381 0 180 arc s .8 g newpath .61905 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.792704 0.141968 0.880079 0.198137 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .47619 0 180 arc s .4 g newpath .2619 .02381 .2381 0 180 arc s .6 g newpath .38095 .02381 .11905 0 180 arc s .8 g newpath .5 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.888816 0.141968 0.97619 0.198137 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .47619 0 180 arc s .4 g newpath .2619 .02381 .2381 0 180 arc s .6 g newpath .61905 .02381 .11905 0 180 arc s .8 g newpath .5 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.203754 0.111184 0.259923 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .2381 0 180 arc s .4 g newpath .38095 .02381 .11905 0 180 arc s .6 g newpath .2619 .02381 .2381 0 180 arc s .8 g newpath .5 .02381 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.119921 0.203754 0.207296 0.259923 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .2381 0 180 arc s .4 g newpath .38095 .02381 .11905 0 180 arc s .6 g newpath .7381 .02381 .2381 0 180 arc s .8 g newpath .5 .02381 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.216033 0.203754 0.303408 0.259923 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .2381 0 180 arc s .4 g newpath .61905 .02381 .35714 0 180 arc s .6 g newpath .5 .02381 .47619 0 180 arc s .8 g newpath .2619 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.312145 0.203754 0.399519 0.259923 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .2381 0 180 arc s .4 g newpath .61905 .02381 .35714 0 180 arc s .6 g newpath .7381 .02381 .2381 0 180 arc s .8 g newpath .2619 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.408257 0.203754 0.495631 0.259923 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .11905 0 180 arc s .4 g newpath .2619 .02381 .2381 0 180 arc s .6 g newpath .14286 .02381 .11905 0 180 arc s .8 g newpath .61905 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.504369 0.203754 0.591743 0.259923 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .11905 0 180 arc s .4 g newpath .2619 .02381 .2381 0 180 arc s .6 g newpath .5 .02381 .47619 0 180 arc s .8 g newpath .61905 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.600481 0.203754 0.687855 0.259923 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .11905 0 180 arc s .4 g newpath .38095 .02381 .11905 0 180 arc s .6 g newpath .14286 .02381 .11905 0 180 arc s .8 g newpath .5 .02381 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.696592 0.203754 0.783967 0.259923 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .11905 0 180 arc s .4 g newpath .38095 .02381 .11905 0 180 arc s .6 g newpath .61905 .02381 .35714 0 180 arc s .8 g newpath .5 .02381 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.792704 0.203754 0.880079 0.259923 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .11905 0 180 arc s .4 g newpath .7381 .02381 .2381 0 180 arc s .6 g newpath .5 .02381 .47619 0 180 arc s .8 g newpath .14286 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.888816 0.203754 0.97619 0.259923 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .11905 0 180 arc s .4 g newpath .7381 .02381 .2381 0 180 arc s .6 g newpath .61905 .02381 .35714 0 180 arc s .8 g newpath .14286 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.26554 0.111184 0.321709 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .7381 .02381 .2381 0 180 arc s .4 g newpath .85714 .02381 .11905 0 180 arc s .6 g newpath .38095 .02381 .35714 0 180 arc s .8 g newpath .14286 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.119921 0.26554 0.207296 0.321709 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .7381 .02381 .2381 0 180 arc s .4 g newpath .85714 .02381 .11905 0 180 arc s .6 g newpath .5 .02381 .2381 0 180 arc s .8 g newpath .14286 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.216033 0.26554 0.303408 0.321709 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .35714 0 180 arc s .4 g newpath .14286 .02381 .11905 0 180 arc s .6 g newpath .38095 .02381 .11905 0 180 arc s .8 g newpath .7381 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.312145 0.26554 0.399519 0.321709 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .35714 0 180 arc s .4 g newpath .14286 .02381 .11905 0 180 arc s .6 g newpath .61905 .02381 .35714 0 180 arc s .8 g newpath .7381 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.408257 0.26554 0.495631 0.321709 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .35714 0 180 arc s .4 g newpath .2619 .02381 .2381 0 180 arc s .6 g newpath .38095 .02381 .11905 0 180 arc s .8 g newpath .61905 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.504369 0.26554 0.591743 0.321709 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .35714 0 180 arc s .4 g newpath .2619 .02381 .2381 0 180 arc s .6 g newpath .7381 .02381 .2381 0 180 arc s .8 g newpath .61905 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.600481 0.26554 0.687855 0.321709 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .35714 0 180 arc s .4 g newpath .5 .02381 .47619 0 180 arc s .6 g newpath .61905 .02381 .35714 0 180 arc s .8 g newpath .38095 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.696592 0.26554 0.783967 0.321709 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .35714 0 180 arc s .4 g newpath .5 .02381 .47619 0 180 arc s .6 g newpath .7381 .02381 .2381 0 180 arc s .8 g newpath .38095 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.792704 0.26554 0.880079 0.321709 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .2381 0 180 arc s .4 g newpath .14286 .02381 .11905 0 180 arc s .6 g newpath .2619 .02381 .2381 0 180 arc s .8 g newpath .7381 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.888816 0.26554 0.97619 0.321709 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .2381 0 180 arc s .4 g newpath .14286 .02381 .11905 0 180 arc s .6 g newpath .5 .02381 .47619 0 180 arc s .8 g newpath .7381 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.327326 0.111184 0.383496 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .11905 0 180 arc s .4 g newpath .38095 .02381 .35714 0 180 arc s .6 g newpath .14286 .02381 .11905 0 180 arc s .8 g newpath .61905 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.119921 0.327326 0.207296 0.383496 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .11905 0 180 arc s .4 g newpath .38095 .02381 .35714 0 180 arc s .6 g newpath .5 .02381 .47619 0 180 arc s .8 g newpath .61905 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.216033 0.327326 0.303408 0.383496 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .11905 0 180 arc s .4 g newpath .5 .02381 .2381 0 180 arc s .6 g newpath .14286 .02381 .11905 0 180 arc s .8 g newpath .5 .02381 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.312145 0.327326 0.399519 0.383496 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .11905 0 180 arc s .4 g newpath .5 .02381 .2381 0 180 arc s .6 g newpath .61905 .02381 .35714 0 180 arc s .8 g newpath .5 .02381 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.408257 0.327326 0.495631 0.383496 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .11905 0 180 arc s .4 g newpath .85714 .02381 .11905 0 180 arc s .6 g newpath .5 .02381 .47619 0 180 arc s .8 g newpath .14286 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.504369 0.327326 0.591743 0.383496 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .11905 0 180 arc s .4 g newpath .85714 .02381 .11905 0 180 arc s .6 g newpath .61905 .02381 .35714 0 180 arc s .8 g newpath .14286 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.600481 0.327326 0.687855 0.383496 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .7381 .02381 .2381 0 180 arc s .4 g newpath .5 .02381 .47619 0 180 arc s .6 g newpath .14286 .02381 .11905 0 180 arc s .8 g newpath .5 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.696592 0.327326 0.783967 0.383496 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .7381 .02381 .2381 0 180 arc s .4 g newpath .5 .02381 .47619 0 180 arc s .6 g newpath .38095 .02381 .35714 0 180 arc s .8 g newpath .5 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.792704 0.327326 0.880079 0.383496 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .7381 .02381 .2381 0 180 arc s .4 g newpath .61905 .02381 .35714 0 180 arc s .6 g newpath .14286 .02381 .11905 0 180 arc s .8 g newpath .38095 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.888816 0.327326 0.97619 0.383496 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .7381 .02381 .2381 0 180 arc s .4 g newpath .61905 .02381 .35714 0 180 arc s .6 g newpath .5 .02381 .2381 0 180 arc s .8 g newpath .38095 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.389113 0.111184 0.445282 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .2619 .02381 .2381 0 180 arc s .4 g newpath .38095 .02381 .35714 0 180 arc s .6 g newpath .5 .02381 .2381 0 180 arc s .8 g newpath .61905 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.119921 0.389113 0.207296 0.445282 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .2619 .02381 .2381 0 180 arc s .4 g newpath .38095 .02381 .35714 0 180 arc s .6 g newpath .85714 .02381 .11905 0 180 arc s .8 g newpath .61905 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.216033 0.389113 0.303408 0.445282 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .2619 .02381 .2381 0 180 arc s .4 g newpath .5 .02381 .47619 0 180 arc s .6 g newpath .61905 .02381 .35714 0 180 arc s .8 g newpath .5 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.312145 0.389113 0.399519 0.445282 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .2619 .02381 .2381 0 180 arc s .4 g newpath .5 .02381 .47619 0 180 arc s .6 g newpath .85714 .02381 .11905 0 180 arc s .8 g newpath .5 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.408257 0.389113 0.495631 0.445282 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .11905 0 180 arc s .4 g newpath .14286 .02381 .11905 0 180 arc s .6 g newpath .38095 .02381 .35714 0 180 arc s .8 g newpath .85714 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.504369 0.389113 0.591743 0.445282 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .11905 0 180 arc s .4 g newpath .14286 .02381 .11905 0 180 arc s .6 g newpath .5 .02381 .47619 0 180 arc s .8 g newpath .85714 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.600481 0.389113 0.687855 0.445282 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .11905 0 180 arc s .4 g newpath .5 .02381 .2381 0 180 arc s .6 g newpath .38095 .02381 .35714 0 180 arc s .8 g newpath .5 .02381 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.696592 0.389113 0.783967 0.445282 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .11905 0 180 arc s .4 g newpath .5 .02381 .2381 0 180 arc s .6 g newpath .85714 .02381 .11905 0 180 arc s .8 g newpath .5 .02381 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.792704 0.389113 0.880079 0.445282 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .11905 0 180 arc s .4 g newpath .61905 .02381 .35714 0 180 arc s .6 g newpath .5 .02381 .47619 0 180 arc s .8 g newpath .38095 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.888816 0.389113 0.97619 0.445282 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .11905 0 180 arc s .4 g newpath .61905 .02381 .35714 0 180 arc s .6 g newpath .85714 .02381 .11905 0 180 arc s .8 g newpath .38095 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.450899 0.111184 0.507068 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .2381 0 180 arc s .4 g newpath .85714 .02381 .11905 0 180 arc s .6 g newpath .5 .02381 .47619 0 180 arc s .8 g newpath .2619 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.119921 0.450899 0.207296 0.507068 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .2381 0 180 arc s .4 g newpath .85714 .02381 .11905 0 180 arc s .6 g newpath .7381 .02381 .2381 0 180 arc s .8 g newpath .2619 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.216033 0.450899 0.303408 0.507068 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .35714 0 180 arc s .4 g newpath .5 .02381 .47619 0 180 arc s .6 g newpath .2619 .02381 .2381 0 180 arc s .8 g newpath .61905 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.312145 0.450899 0.399519 0.507068 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .35714 0 180 arc s .4 g newpath .5 .02381 .47619 0 180 arc s .6 g newpath .38095 .02381 .35714 0 180 arc s .8 g newpath .61905 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.408257 0.450899 0.495631 0.507068 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .35714 0 180 arc s .4 g newpath .7381 .02381 .2381 0 180 arc s .6 g newpath .2619 .02381 .2381 0 180 arc s .8 g newpath .38095 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.504369 0.450899 0.591743 0.507068 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .35714 0 180 arc s .4 g newpath .7381 .02381 .2381 0 180 arc s .6 g newpath .61905 .02381 .11905 0 180 arc s .8 g newpath .38095 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.600481 0.450899 0.687855 0.507068 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .35714 0 180 arc s .4 g newpath .85714 .02381 .11905 0 180 arc s .6 g newpath .38095 .02381 .35714 0 180 arc s .8 g newpath .2619 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.696592 0.450899 0.783967 0.507068 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .61905 .02381 .35714 0 180 arc s .4 g newpath .85714 .02381 .11905 0 180 arc s .6 g newpath .61905 .02381 .11905 0 180 arc s .8 g newpath .2619 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.792704 0.450899 0.880079 0.507068 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .2619 .02381 .2381 0 180 arc s .4 g newpath .14286 .02381 .11905 0 180 arc s .6 g newpath .5 .02381 .2381 0 180 arc s .8 g newpath .85714 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.888816 0.450899 0.97619 0.507068 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .2619 .02381 .2381 0 180 arc s .4 g newpath .14286 .02381 .11905 0 180 arc s .6 g newpath .61905 .02381 .35714 0 180 arc s .8 g newpath .85714 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.512685 0.111184 0.568854 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .11905 0 180 arc s .4 g newpath .2619 .02381 .2381 0 180 arc s .6 g newpath .38095 .02381 .35714 0 180 arc s .8 g newpath .85714 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.119921 0.512685 0.207296 0.568854 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .11905 0 180 arc s .4 g newpath .2619 .02381 .2381 0 180 arc s .6 g newpath .5 .02381 .47619 0 180 arc s .8 g newpath .85714 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.216033 0.512685 0.303408 0.568854 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .11905 0 180 arc s .4 g newpath .61905 .02381 .11905 0 180 arc s .6 g newpath .38095 .02381 .35714 0 180 arc s .8 g newpath .5 .02381 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.312145 0.512685 0.399519 0.568854 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .11905 0 180 arc s .4 g newpath .61905 .02381 .11905 0 180 arc s .6 g newpath .85714 .02381 .11905 0 180 arc s .8 g newpath .5 .02381 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.408257 0.512685 0.495631 0.568854 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .11905 0 180 arc s .4 g newpath .7381 .02381 .2381 0 180 arc s .6 g newpath .5 .02381 .47619 0 180 arc s .8 g newpath .38095 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.504369 0.512685 0.591743 0.568854 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .11905 0 180 arc s .4 g newpath .7381 .02381 .2381 0 180 arc s .6 g newpath .85714 .02381 .11905 0 180 arc s .8 g newpath .38095 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.600481 0.512685 0.687855 0.568854 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .2381 0 180 arc s .4 g newpath .38095 .02381 .35714 0 180 arc s .6 g newpath .2619 .02381 .2381 0 180 arc s .8 g newpath .7381 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.696592 0.512685 0.783967 0.568854 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .2381 0 180 arc s .4 g newpath .38095 .02381 .35714 0 180 arc s .6 g newpath .5 .02381 .47619 0 180 arc s .8 g newpath .7381 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.792704 0.512685 0.880079 0.568854 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .2381 0 180 arc s .4 g newpath .61905 .02381 .11905 0 180 arc s .6 g newpath .2619 .02381 .2381 0 180 arc s .8 g newpath .5 .02381 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.888816 0.512685 0.97619 0.568854 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .2381 0 180 arc s .4 g newpath .61905 .02381 .11905 0 180 arc s .6 g newpath .7381 .02381 .2381 0 180 arc s .8 g newpath .5 .02381 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.574471 0.111184 0.63064 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .47619 0 180 arc s .4 g newpath .7381 .02381 .2381 0 180 arc s .6 g newpath .38095 .02381 .11905 0 180 arc s .8 g newpath .5 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.119921 0.574471 0.207296 0.63064 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .47619 0 180 arc s .4 g newpath .7381 .02381 .2381 0 180 arc s .6 g newpath .61905 .02381 .11905 0 180 arc s .8 g newpath .5 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.216033 0.574471 0.303408 0.63064 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .47619 0 180 arc s .4 g newpath .85714 .02381 .11905 0 180 arc s .6 g newpath .5 .02381 .2381 0 180 arc s .8 g newpath .38095 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.312145 0.574471 0.399519 0.63064 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .47619 0 180 arc s .4 g newpath .85714 .02381 .11905 0 180 arc s .6 g newpath .61905 .02381 .11905 0 180 arc s .8 g newpath .38095 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.408257 0.574471 0.495631 0.63064 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .14286 .02381 .11905 0 180 arc s .4 g newpath .2619 .02381 .2381 0 180 arc s .6 g newpath .61905 .02381 .11905 0 180 arc s .8 g newpath .85714 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.504369 0.574471 0.591743 0.63064 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .14286 .02381 .11905 0 180 arc s .4 g newpath .2619 .02381 .2381 0 180 arc s .6 g newpath .7381 .02381 .2381 0 180 arc s .8 g newpath .85714 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.600481 0.574471 0.687855 0.63064 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .14286 .02381 .11905 0 180 arc s .4 g newpath .38095 .02381 .35714 0 180 arc s .6 g newpath .61905 .02381 .11905 0 180 arc s .8 g newpath .7381 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.696592 0.574471 0.783967 0.63064 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .14286 .02381 .11905 0 180 arc s .4 g newpath .38095 .02381 .35714 0 180 arc s .6 g newpath .85714 .02381 .11905 0 180 arc s .8 g newpath .7381 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.792704 0.574471 0.880079 0.63064 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .14286 .02381 .11905 0 180 arc s .4 g newpath .5 .02381 .47619 0 180 arc s .6 g newpath .7381 .02381 .2381 0 180 arc s .8 g newpath .61905 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.888816 0.574471 0.97619 0.63064 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .14286 .02381 .11905 0 180 arc s .4 g newpath .5 .02381 .47619 0 180 arc s .6 g newpath .85714 .02381 .11905 0 180 arc s .8 g newpath .61905 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.636257 0.111184 0.692427 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .2619 .02381 .2381 0 180 arc s .4 g newpath .7381 .02381 .2381 0 180 arc s .6 g newpath .61905 .02381 .35714 0 180 arc s .8 g newpath .5 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.119921 0.636257 0.207296 0.692427 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .2619 .02381 .2381 0 180 arc s .4 g newpath .7381 .02381 .2381 0 180 arc s .6 g newpath .85714 .02381 .11905 0 180 arc s .8 g newpath .5 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.216033 0.636257 0.303408 0.692427 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .35714 0 180 arc s .4 g newpath .5 .02381 .2381 0 180 arc s .6 g newpath .38095 .02381 .11905 0 180 arc s .8 g newpath .7381 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.312145 0.636257 0.399519 0.692427 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .35714 0 180 arc s .4 g newpath .5 .02381 .2381 0 180 arc s .6 g newpath .61905 .02381 .35714 0 180 arc s .8 g newpath .7381 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.408257 0.636257 0.495631 0.692427 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .35714 0 180 arc s .4 g newpath .61905 .02381 .11905 0 180 arc s .6 g newpath .38095 .02381 .11905 0 180 arc s .8 g newpath .61905 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.504369 0.636257 0.591743 0.692427 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .35714 0 180 arc s .4 g newpath .61905 .02381 .11905 0 180 arc s .6 g newpath .7381 .02381 .2381 0 180 arc s .8 g newpath .61905 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.600481 0.636257 0.687855 0.692427 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .35714 0 180 arc s .4 g newpath .85714 .02381 .11905 0 180 arc s .6 g newpath .61905 .02381 .35714 0 180 arc s .8 g newpath .38095 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.696592 0.636257 0.783967 0.692427 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .38095 .02381 .35714 0 180 arc s .4 g newpath .85714 .02381 .11905 0 180 arc s .6 g newpath .7381 .02381 .2381 0 180 arc s .8 g newpath .38095 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.792704 0.636257 0.880079 0.692427 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .47619 0 180 arc s .4 g newpath .61905 .02381 .35714 0 180 arc s .6 g newpath .38095 .02381 .11905 0 180 arc s .8 g newpath .61905 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.888816 0.636257 0.97619 0.692427 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .5 .02381 .47619 0 180 arc s .4 g newpath .61905 .02381 .35714 0 180 arc s .6 g newpath .5 .02381 .2381 0 180 arc s .8 g newpath .61905 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.698043 0.111184 0.754213 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .14286 .02381 .11905 0 180 arc s .4 g newpath .38095 .02381 .11905 0 180 arc s .6 g newpath .61905 .02381 .11905 0 180 arc s .8 g newpath .85714 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.119921 0.698043 0.207296 0.754213 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .14286 .02381 .11905 0 180 arc s .4 g newpath .38095 .02381 .11905 0 180 arc s .6 g newpath .7381 .02381 .2381 0 180 arc s .8 g newpath .85714 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.216033 0.698043 0.303408 0.754213 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .14286 .02381 .11905 0 180 arc s .4 g newpath .5 .02381 .2381 0 180 arc s .6 g newpath .61905 .02381 .11905 0 180 arc s .8 g newpath .7381 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.312145 0.698043 0.399519 0.754213 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .14286 .02381 .11905 0 180 arc s .4 g newpath .5 .02381 .2381 0 180 arc s .6 g newpath .85714 .02381 .11905 0 180 arc s .8 g newpath .7381 .02381 .2381 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.408257 0.698043 0.495631 0.754213 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .14286 .02381 .11905 0 180 arc s .4 g newpath .61905 .02381 .35714 0 180 arc s .6 g newpath .7381 .02381 .2381 0 180 arc s .8 g newpath .61905 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.504369 0.698043 0.591743 0.754213 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .14286 .02381 .11905 0 180 arc s .4 g newpath .61905 .02381 .35714 0 180 arc s .6 g newpath .85714 .02381 .11905 0 180 arc s .8 g newpath .61905 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.600481 0.698043 0.687855 0.754213 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .2619 .02381 .2381 0 180 arc s .4 g newpath .38095 .02381 .11905 0 180 arc s .6 g newpath .5 .02381 .2381 0 180 arc s .8 g newpath .85714 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.696592 0.698043 0.783967 0.754213 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .2619 .02381 .2381 0 180 arc s .4 g newpath .38095 .02381 .11905 0 180 arc s .6 g newpath .61905 .02381 .35714 0 180 arc s .8 g newpath .85714 .02381 .11905 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.792704 0.698043 0.880079 0.754213 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .2619 .02381 .2381 0 180 arc s .4 g newpath .61905 .02381 .11905 0 180 arc s .6 g newpath .5 .02381 .2381 0 180 arc s .8 g newpath .61905 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.888816 0.698043 0.97619 0.754213 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.214286 0.238095 0.0238095 0.238095 [ [ 0 0 0 0 ] [ 1 .64286 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .64286 L 0 .64286 L closepath clip newpath .2 g .5 Mabswid newpath .2619 .02381 .2381 0 180 arc s .4 g newpath .61905 .02381 .11905 0 180 arc s .6 g newpath .85714 .02381 .11905 0 180 arc s .8 g newpath .61905 .02381 .35714 0 180 arc s MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{287.938, 222.438}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgGooOol00goo00=:DWooOol0 0goo00GooOol00goo00DDaGooOomoofLi00Eoo`03BU9oogoo00=oo`03@05Ool00fLiOomoo`03Ool00c6GooOol00goo00GooOol00goo00GooOol00goo00=:DWooOol00goo00@=oo`03IcUoogoo00Eoo`06GooOomoofLiBU85Ool00aC5@05Ool00c6@06Ool0 0dYBGooBU9oodYB00=oo`05GooIcUoodYB00Eoo`065GooIcT01goo00DaS7oo5GooOol00goo00HaS7ooBU9oodYBIcT5Ool01S6GooIcT7Ool01DYBOolaS7ooGooIcT00goo00=:DWooBU800goo 00GooOol00Woo00GooOol017oo00=:DWooDYBOol0 0goo00@aS7ooOomW>@Eoo`05Goo Ool02Goo00GooOol00goo00=:DWooOol00goo00@DaGoo OomW>@Eoo`035GooOol00goo00Ool3BU83Ool2BU80 11C5Oomoogoo0QC51goo00GooOol02Goo00=W>Goo5GooOol01Woo0dYB00=oofLi5Ool2GooOol00goo00=W>GooOol00goo00=:DWooOol00goo 00DDaGooOomooc6<00Eoo`03IcUoogoo00=oo`03IcUoogoo00=oo`03BU9oogoo009oo`055GooOol00goo00=W>GooOol00goo00@DaGooOomW>@Eoo`03@05Ool00c6GooOol00goo00=:DWoo Ool00goo00DDaGooOomoofLi00Eoo`03GooOol00goo00GooOol00goo00GooOomoofLiOom:DP03Ool00dYBOomoo`03Ool00aC5Oomoo`02Ool01TYBOomoogooGoo009oo`03IcUoogoo00Aoo`065Goo OomoofLi00Eoo`065DYB17oo00GooOol0 0goo00DDaGooOomoofLi00Eoo`035Goo00=oo`035@05Ool00c6GooOol00goo00DDaGooOomoodYB00Eoo`03IcUo ogoo009oo`03@03Ool014YB Oom:DS6<1Goo00@06 Ool00aC5Oomoo`02Ool01dYBOolaS7ooGooOol00goo00GooOol00goo00=:DWooOol00Woo00GooOol00goo00GooOom:DWooBU8aS005Ool00aC5Oomoo`02Ool0136Goo Ool00Woo00GooOol00goo00HDaGooOomooc6GooBU801Goo00DYBOol00goo00DDaGoo@05Ool00aC5Oomoo`02Ool00dYBIcUoo`03Ool01AC5GooOol00goo00@aS7ooOomW>@Aoo`03BU8a S7oo00Eoo`035GooOolaS09oo`055GooOolaS09oo`045@05Ool00aC5Oomoo`07Ool000Uoo`03FLi00=oo`=W>@=oo`8aS003Oom:DWoo00=oo`035@=oo`9W>@04@03Ool3IcT3Ool35@03Ool2IcT014YBOomoogoo0QC52Woo0009Ool00aC5@02IcT00goo5@Aoo`8Da@9oo`9W>@Aoo`035@Aoo`8Da@9oo`9W>@Aoo`8Da@Yoo`9:DPAoo`8Da@9oo`9:DPAoo`8Da@moo`8Da@Qoo`8D aBIoo`03BU9oogoo00Ioo`9:DQ5oo`002goo00@DaGoo@=oo`=W>@=oo`@9oo`=W>@035@=oo`@Aoo`8DaAAoo`9:DP=oo`GooOol00goo00=W>GooOol00Woo00@05Ool00dYBOomoo`03Ool00fLiOomo o`03Ool00aC5Oomoo`03Ool0136GooOol00goo00=:DWooOol00goo00GooOol00goo00=W>GooOol00goo00@DaGooOolaS0Eoo`03IcUoogoo 00=oo`03BU9oogoo00=oo`03IcUoogoo00=oo`055GooOomoofLiBU85Ool0 1QC5Oomoogoo5GooOol00goo00Goo009oo`03IcUoogoo00Aoo`03BU9oogoo00Aoo`065Goo OomoofLiOom:DP03Ool00dYBGooOomoofLiBU85Ool011C5Oomooc6<1Goo00=W>DYBOol00Woo00=:DS6Goo Ool00goo00DDaGooOomooc6<00Eoo`03IcUoogoo00=oo`03Goo00Aoo`03 5DYB1goo00DDaGoo5GooOol01Goo00DDaGoo5GooIcT7Ool00dYBGooIcT00goo 00E:DWooBU9ooc6<00Moo`045Goo IcT01goo00/DaGooOomooaC5OolaS7ooGooBU800goo00GooOol01Woo00GooOol00goo 00HaS7ooOom:DWooIcT9Ool00aC5OolaS004Ool00dYBOomW>@08Ool00dYBGooOol00goo00A:DWooOolaS0Qoo`035GooBU801Goo 00GooBU800Woo00GooOol00goo 00DDaGooOomooc6<00Eoo`03IcUoogoo009oo`07GooOol00Woo00Da S7ooOomoofLi00aoo`03GooOol00goo00GooOolaS0Eoo`03IcUoogoo 00Aoo`035GooOol00goo00GooOol00goo00@aS7ooOomW>@]oo`03GooOol00goo00GooGooOol017oo00Ool00c6Ool00aC5Oomoo`07Ool00aC5Oomoo`0>Ool00aC5Oomo o`08Ool00aC5Oomoo`0>Ool00aC5Oomoo`07Ool00aC5Oomoo`0>Ool00aC5Oomoo`09Ool000aoo`03 GooOomoofLi00Eo o`03@05Ool00c6GooOol00goo00GooOomoodYB00Eoo`03IcUoogoo00=oo`03GooOomW >@Eoo`03IcUoogoo00=oo`03@05Ool00fLi Oomoo`03Ool00c6@05Ool00aC5@Aoo`03@05Ool00c6@Eoo`03@05Ool00dYBDYB1Goo 00@05Ool01aC5OolaS7ooGooOol00goo00GooIcT8Ool0136<5GooIcUo odYB00Eoo`05Goo009oo`03BU9oofLi00Aoo`05@05Ool00aC5Oomoo`03Ool00c6GooOol00Woo00=W>GooBU801Goo00GooOomoofLi00Ioo`03BU9ooc6<00Eoo`035GooOol00Woo00DaS1C5OomoofLi009oo`04BU9oogoo5GooOol00goo00=:DS6GooOomooc6<00aoo`03IcUo ogoo009oo`03IcUoogoo01=oo`03IcUoogoo00=oo`03IcUoogoo00=oo`03BU9oogoo00eoo`03IcUo ogoo009oo`03BU9oogoo00Yoo`03GooBU801Goo00=:DWooOol00goo00GooOol00goo00=W>GooOol017oo00GooOol00Woo 00C6GooOol017oo00=:DWooGooDYBOol00goo00=W>GooOol04goo 00=W>GooOol00goo00=W>GooOol017oo00=:DWooOol02goo00=:DVLiOol00goo00=:DWooOol02goo 00@04IcT00c6<5@Qoo`03IcUo ogoo00Moo`03BU9oogoo00Aoo`9W>@Qoo`9W>@03Oom:DWoo00Eoo`03IcUoogoo015oo`03IcUoogoo 00Eoo`03IcUoogoo00Aoo`9:DPQoo`9:DP03OomW>Goo00Eoo`03BU9oogoo015oo`03BU9oogoo00eo o`03BU9oogoo00Ioo`9:DP]oo`002Woo00=W>GooOol03goo00=W>GooOol01goo00=W>GooOol03Woo 00=W>GooOol01goo00=:DWooOol01Woo00Ool00fLiOomoo`08Ool00dYB Oomoo`06Ool5Ool00fLiOomoo`07Ool00fLiOomoo`06Ool6BU82Ool00fLiOomoo`08 Ool00dYBOomoo`0>Ool00dYBOomoo`0@Ool6BU8>Ool000aoo`03IcUoogoo00]oo`03IcUoogoo00Yo o`9W>@aoo`9W>@aoo`9:DPaoo`9:DT9oo`9:DPaoo`9:DPaoo`9W>@aoo`9W>@]oo`9W>@aoo`9W>@ao o`9:DPaoo`9:DRMoo`003Goo0fLi1goo0fLi3goo0VLi27oo0VLi47oo0TYB1goo0dYBAWoo0TYB27oo 0TYB47oo0VLi27oo0VLi3goo0VLi27oo0VLi47oo0TYB27oo0TYB:Goo000@Ool7IcTDOol8IcTDOol7 BU9;Ool8BU8DOol8IcTCOol8IcTDOol8BU8[Ool00?moob1oo`00ogoo87oo003oOolPOol00?moob1o o`00ogoo87oo0007Ool00fLiOomoo`03Ool00fLiOomoo`03Ool00aC5Oomoo`03Ool00dYBOomoo`03 Ool01C6GooOol00goo00GooOol0 0goo00=:DWooOol00goo00GooOomooc6<00Eoo`03IcUoogoo00=oo`03BU9o ogoo00=oo`035GooOol00goo00=W>GooOol00goo00Goo009oo`03IcUoogoo00Aoo`035DYB1Goo00GooOomooaC5GooOomoofLiBU85Ool00aC5Oomoo`02 Ool00dYBOomoo`02Ool01dYBOomoogooGoo00=oo`035GooOol00Woo00DYBOol0 1Woo0007Ool01DYBOomW>GooIcT01goo00GooBU801Goo00GooOol00Woo00GooOomooaC5OolaS7ooGooBU9oodYBOolaS005 Ool00aC5Oomoo`03Ool01FLiOomoogooGooOol00Woo00GooOol00Woo00GooBU801Goo00Goo00=oo`035GooOomooaC500Aoo`03IcU:DWoo00=oo`035Goo00=oo`03GooOolDa@Eo o`03IcUoogoo00=oo`03BU9ooc6<00=oo`035GooOol017oo00GooGooOol017oo00GooOolaS09oo`04 BU9oogoo5GooOolDa@Eoo`03IcUoogoo00=oo`03BU9oogoo00Aoo`035@=oo`9W>@Moo`035@=oo`9W>@03BU9oogoo00Aoo`035@03Ool3IcT7Ool0 0dYBOomoo`04Ool25@03Ool2IcT00dYBOomoo`07Ool000Yoo`03BU9oogoo00Uo o`03BU9ooaC5008DaA=oo`=:DP=oo`@Yoo`035@03Oom:DWoo00Moo`035Goo00Eoo`035Goo00Ioo`03@Yoo`03BU9oogoo00Ioo`@9oo`03BU9oogoo00Moo`002goo0TYB1goo0TYB;7oo0QC5 27oo00GooOol027oo0QC517oo0VLi0Woo0QC517oo0VLi2Goo00 Ool00dYBOomoo`09Ool000ioo`E:DS9oo`HDaAEoo`HDa@I:DQ1oo`HDa@IW>@moo`HDa@IW>@ioo`03 Ool00;Moo`GooOomoofLi 00Eoo`03BU9oogoo00=oo`035GooOol00goo00GooOol00goo00DaS7ooOomo ofLi00Eoo`03BU9oogoo00=oo`035GooOol017oo00DDaGooOolDaC6<00Eoo`06IcUoogooOomW>DYB0goo00=:DWooGooOol01Goo00LDaGooOomooaC5OolaS003Ool00c6@05Ool00aC5Oomoo`02Ool00fLiOomoo`03Ool01C6GooOol00goo00DYBOol00goo00GooOomoodYBOolaS005Ool00aC5Oomo o`02Ool00fLiOomoo`03Ool01C6GooOol017oo00@DaGoo5GooOomoofLi00Eo o`03BU9oogoo00Eoo`045@09Ool00aC5OolDa@03 Ool01C6GooIcUoodYB00Moo`035GooOol00goo00GooOol00goo00HaS7ooOomooc6< BU84Ool00fLiOomoo`03Ool00aC5Oomoo`02Ool00fLiOomoo`03Ool00c6GooOol00goo00Goo Ool00Woo00=:DS6GooOol00goo00@0;Ool00aC5Oomoo`03Ool00c6GooOol00goo00@DaGooOomW>@Eo o`03GooOol00goo00=:DWooOol00goo00DDaGooOom:DVLi00Aoo`035GooOol01Goo00GooOol017oo00=:DWooOol00goo00=W>Goo Ool01Woo00DYBOol00goo00=W>GooOol017oo00GooOol00goo00=W>GooOol00goo00=:DWooOol01Woo00GooOol00goo00Goo Ool00goo00GooOol00goo00@Eoo`03GooOol01Goo00GooOol017oo 00GooOol01Woo00GooOol017oo00=W>GooOol017oo 1c6<1Woo00=W>GooOol01Goo00=W>GooOol00Woo00=:DS6<GooOol017oo00=: DWooOol04Goo00=:DWooOol02Woo00=:DWooOol037oo00=:DWooOol017oo00Goo Ool00goo00AC55GooOol00goo00AC55@03OolaS36< 00Aoo`9W>@Yoo`03BU8aS7oo00=oo`9W>@9oo`8aS0Aoo`9W>@Uoo`03IcUoogoo00moo`03IcUoogoo 00Moo`03IcUoogoo00=oo`9:DPQoo`9:DP03IcUoogoo00Ioo`03BU9oogoo00moo`03BU9oogoo00eo o`9:DPQoo`9:DPUoo`03@Aoo`8aS09oo`9W>@Aoo`8aS0Yoo`9W>@Aoo`03@Aoo`8aS0]oo`00 3Goo1S6<1fLi37oo00=:DWooGooOol03Woo00=W>GooOol0 1goo00=W>GooOol01Goo24YB00=oofLiOol02Goo00=:DWooOol03Woo00=:DWooOol03goo24YB37oo 00@Yoo`03IcUoogoo00eoo`03IcUoogoo00Qoo`03IcUoogoo00ioo`03BU9oogoo00Qoo`03BU9o ogoo02Uoo`03GooOol00goo00GooOomooc6<00Eoo`03IcUoogoo00=oo`035GooOol00goo00GooOol00goo00A:DWooOom:DPEoo`03 GooOomoofLi00Eoo`03GooOol00goo00=:DWooOol01Goo 0007Ool00c6<5GooOol00Woo00GooOol00goo00E:DWooOomooc6<00Eo o`03IcUoogoo009oo`035GooOol00Woo00=:DS6GooOomoofLiBU82Ool00fLiBU9oo`04Ool01C6GooOomoofLi00Eoo`03GooOom:DVLi1Goo00DaS7ooOomooaC500Ioo`03IcUoogoo00=oo`05BU9oogoo OomW>@05Ool00c6<5Goo00=oo`035GooIcT01Goo00E:DWooGooOomoofLi00Eoo`05GooOol00Woo00GooOomooaC500Ioo`04GooOolDa@05Ool00fLiOomoo`03Ool00dYBGooOol00Woo00=:DWooGooOol00goo00GooOol00goo00=:DWooOol00Woo 00=W>GooOol00goo00GooOomoodYBOolaS008Ool000Qoo`03GooOol00Woo00Goo00Aoo`03IcUoogoo00Aoo`03BU8aS7oo00Aoo`03Goo00Ao o`03GooBU8014YB00=ooc6< Ool017oo00=W>GooOol017oo00AC5Ool01Woo00Goo Ool017oo00GooOol01Goo1S6<00=oodYBOol00goo00=W>GooOol01Goo00=W>GooOol01Goo1C6<1goo 00=W>GooOol017oo00=W>GooOol00goo00GooOol00Woo00=:DS6GooOol00goo00GooOol00goo00@04Ool2@03@aoo`8aS0Aoo`9W >@8aS0Aoo`9W>@Yoo`03FLi17oo0S6<0VLi 17oo0S6<00=:DWooOol02Goo0VLi0goo0S6<0VLi17oo0S6<37oo000>Ool5@03IcT@ Ool6Ool00c6Ool00dYBOomoo`08Ool00fLiOomoo`06BU88Ool00fLiOomoo`07 Ool00fLiOomoo`0>Ool00fLiOomoo`08Ool00dYBOomoo`06IcT6Ool004=oo`8aS0aoo`8aS0]oo`8aS0aoo`8aS2Moo`9:DPaoo`9:DPaoo`9W>@aoo`9W>@]oo`9W >@aoo`9W>@aoo`9:DPaoo`9:DRMoo`00AGoo0S6<1goo0c6<3goo0S6<27oo0S6<:goo0TYB27oo0TYB 47oo0VLi27oo0VLi3goo0VLi27oo0VLi47oo0TYB27oo0TYB:Goo0017Ool7GooOol00goo00GooOol00goo00DaS7ooOomoofLi00Eoo`035GooOol00goo00=:DWooOol00goo00@aS7ooOola S0Eoo`03BU9oogoo00=oo`035Goo009oo`03IcUoogoo00Aoo`05GooOol00Woo00GooOol00goo00=:DS6< Ool00Woo00GooOol00goo00GooBU800goo00=:DWoo GooOol00goo00GooOol00Woo00PDaGooOolaS7oo GooOol00goo00DYBOol00goo00LDaGooGooIcT01goo00DaS7ooOomoodYB00Eo o`035@05Ool00aC5Oomoo`03Ool01c6GooOol00goo00GooOom:DWooBU83Ool01C6< OolaS7oo5@05Ool01aC5OolaS7oo@04Ool00aC5Oomoo`02Ool00c6@Eo o`03@04Ool00c6<5@07Ool00aC5OolaS003Ool014YBOomooaC52Woo00=W>GooBU8027oo0008 Ool00dYBIcUoo`04Ool00aC5OomW>@05Ool00aC5Oomoo`04Ool00dYBOomoo`03Ool00fLiOomoo`03 Ool011C5OomoofLi0Woo00A:DWooOolDa@Eoo`03BU9oogoo00=oo`03GooOol00goo00@DaGoo OomW>@Eoo`03BU9oogoo00=oo`035FLi0goo0VLi00@DaGooOomoo`8Da@Moo`03 BU9oogoo00Aoo`=W>@=oo`9W>@045DYBBU800goo0TYB1Goo00GooOol00goo00GooOomoo`8aS0035FLi00=oo`=W>@Ioo`03BU9o ogoo009oo`035@=oo`9W>@aoo`035GooBU800TYB00=ooaC5Ool01Goo00IW>C6<@02IcT00goo5@Aoo`8Da@9oo`9W>@Aoo`035@Aoo`8Da@9oo`9W>@Aoo`8Da@Yoo`9:DPAoo`8D a@9oo`9:DPAoo`8Da@moo`8Da@Qoo`8DaBaoo`03BU9oogoo00Ioo`9:DP]oo`002Woo0TYB3goo0TYB 97oo0S6<1goo00Goo00Aoo`035Goo00Aoo`035GooOol00goo00EW>GooOomoodYB00Eoo`035@05Ool00aC5Oomoo`03Ool00c6< Oomoo`03Ool00dYBOomoo`03Ool01FLiOomoogooIcT01Goo00GooOomW>@Eoo`035@05Ool00aC5Oomoo`03Ool00c6GooOol00goo00GooOomoodYB00Eoo`03 5GooOol01Goo0007Ool00dYBGoo009oo`03IcUoogoo009oo`03BU9oogoo00Aoo`055Goo OomoofLi00Ioo`075GooOomoofLi00Ioo`07 5GooOol00goo00E:DWooOomoofLi00Ioo`065GooBU800goo00=:DWooOol00Woo00=:DWooOol00goo00GooOomoodYB00Eoo`035@05Ool00aC5Oomoo`03Ool00dYB@Eo o`03BU9oogoo00Eoo`045GooBU800goo00=W>DYBOol01Goo00@07Ool00aC5OolDa@03Ool00c6Goo00=oo`03GooOol00Woo00GooOol00Woo00=W>GooOol00goo00@07Ool00dYBOomoo`05Ool00aC5GooOol01Goo 00GooOol00goo00=W>GooOol01Goo00GooOol01Goo00@Eo o`03BU9oogoo00=oo`03IcUoogoo00Eoo`055GooOol00goo00=:DWooOol0 0goo00GooOolDaC6<00Aoo`03IcU:DWoo00=oo`03IcU:DWoo00Aoo`045@05 Ool00c6GooOol00goo00=W>GooOol017oo00@Qoo`03 BU9oogoo00Aoo`8Da@=oo`035FLi00=oo`9W>@03BU9oogoo00Aoo`03IcU:DTYB00=oo`=:DP=o o`DYBOol02Woo00=:DWooOol017oo00=W>GooOol01Goo00=W>GooOol04Goo00=W>GooOol0 17oo00=:DVLiOol02Woo00=W>GooGooOol02Woo00=W>Goo @Yoo`03BU8aS7oo00Ioo`@9oo`03BU9oogoo00Aoo`03IcUoogoo00=:DP=oo`DYBBU8027oo00=:DWooOol017oo00=W>GooOol01goo00=W>GooOol0 3goo00=W>GooOol01Woo00=:DVLiIcT027oo00=W>GooOol017oo00=:DWooOol01goo0VLi27oo0VLi 47oo0S6<27oo0S6<3goo00=:DS6GooOol03goo00=W >GooOol01goo00=W>GooOol03goo00=W>GooOol027oo000=Ool2BU83Ool2BU8BOol00dYBOomoo`0> Ool00dYBOomoo`08Ool016LiOom:DTYB0goo0dYB1goo00=W>GooOol01goo00=W>GooOol03Woo00=W >GooOol027oo00A:DWooIcUW>@=oo`=W>@Moo`03BU9oogoo00Uoo`=W>@9oo`=W>AAoo`GooOol00dYB2Goo00=W>GooOol02Goo00=W>GooOol037oo00=W>GooOol02Woo00=:DWooOol0 0fLi2Goo00=:DWooOol03Goo0VLi6Woo0S6<5Goo00A:DWooOomoo`GooOol02goo00=W>GooOol02Woo00=W>GooOol037oo00=: DWooOol02Woo00=:DWooOol0@Woo00=:DWooOol02Woo00=:DWooOol037oo00=W>GooOol02Woo00=W >GooOol02goo00=W>GooOol02Woo0VLi37oo000YOol5BU83Ool4BU8@Ool4IcT3Ool5IcT?Ool5IcT3 Ool4IcT@Ool4BU83Ool5BU96Ool5BU83Ool4BU8@Ool4IcT3Ool5IcT?Ool5IcT3Ool4IcT>Ool002io o`=:DQQoo`=W>AUoo`=W>AQoo`=:DU1oo`=:DQQoo`=W>AUoo`=W>A9oo`00ogoo87oo003oOolPOol0 0?moob1oo`00ogoo87oo0007Ool00aC5Oomoo`03Ool00fLiOomoo`03Ool00dYBOomoo`03Ool00fLi Oomoo`03Ool01C6GooOol00goo00=:DWooOol00Woo00=W>GooOol00goo 00DaS7ooOomooaC500Eoo`03IcUoogoo00=oo`03IcUoogoo00=oo`03BU9oogoo00=oo`05GooOol00goo00EW>GooOomooc6<00Eoo`035GooOol00goo00=:DWoo Ool00goo00AW>GooOolaS0Eoo`035@Eoo`05GooOol00Woo00GooOomoofLiBU83Ool01C6DYBOol00Woo00=:DS6GooOomooc6<5Goo009oo`03IcUoogoo00Aoo`06BU9oogooOola S1C50goo00GooOomoofLiOom:DP03Ool00dYBGooOol00goo00GooOol00goo00HaS7ooBU9oodYBIcT5Ool01C6@Mo o`07BU9ooc6GooIcT00goo00=:DWooBU800goo00@a S7ooGooIcT01Goo00DaS7oo5DYBOom:DWoo@Aoo`04GooIcT00goo00E: DWooBU9ooc6<00Moo`001goo00GooOom:DP9oo`03GooOol00goo00=:DWooOol00goo00GooOol00goo00@aS7oo OomW>@Eoo`03GooOol00goo00GooOomooc6<00Aoo`03IcUoogoo00=oo`03GooOol00goo00GooOol00goo00@aS7ooOomW>@Eoo`03GooOol01Goo00GooGooOol00goo 00Ool00aC5Oomoo`08Ool00aC5Oomoo`0>Ool00aC5 Oomoo`07Ool00aC5Oomoo`0>Ool00aC5Oomoo`11Ool8Ool00c6< Oomoo`07Ool00c6Ool00c6GooOol00goo 00GooOol00Woo00E:DWooOomooaC500Eoo`03BU9oogoo00=oo`03IcUoogoo 00=oo`03GooOol00goo00=:DWooOol00goo00GooOomooaC500Eoo`03IcUoogoo00=oo`03BU9oogoo00=oo`03Goo Ool00goo00=W>GooOol00goo00GooOomooaC500Eoo`03BU9oogoo00=oo`03IcUoogoo009oo`03GooOol00goo00=:DS6GooOol00Woo 00GooOol017oo00GooOomoofLiBU85Ool00aC5GooOol0 0Woo00GooOomooaC500Eoo`05IcUoodYBOom:DP03Ool01C6GooOomooaC500Eoo`03IcUoogoo00=oo`07BU9ooc6GooOol0 0Woo00GooIcUoodYB00Eoo`065DYB1Woo00GooOolaS0Eoo`03IcUoogoo009oo`035DYBOol01Goo 00@05Ool00dYBOomo o`04Ool00aC5Oomoo`03Ool016LiOomooaC50Woo00@aS7ooOomW>@Eoo`03GooOol017oo00FLi00=W>@03 OolaS36<00@HaS0Uoo`035FLi00=W >@Uoo`035@03BU9oogoo00Ioo`035GooOol027oo 0QC517oo0VLi0Woo0QC517oo0VLi2Woo0QC517oo0TYB0Woo0QC517oo0TYB2Woo00Uoo`035GooOol00goo00EW >GooOomooaC500Eoo`03GooOol00goo00=W>GooOol00goo00E:DWooOomooaC500Eoo`03GooOol0 0goo00AW>GooOolDa@Eoo`03IcUoogoo00=oo`03GooOol00goo00LD aGooOomooaC5OolaS003Ool00c6GooOomoodYBGooOomoofLi00Io o`03BU9oogoo009oo`065GooOomoofLiOom:DP03Ool00dYBOomoo`02 Ool00aC5Oomoo`03Ool01TYBOomoogooGoo009oo`03IcUoogoo009oo`035DYB0goo00GooOol00Woo00GooOomooaC500Eoo`03IcUoogoo 009oo`035Goo00Ioo`002Goo00GooIcT01goo00@05Ool00aC5Oomoo`03Ool01TYBOolaS7oo@07Ool000Yoo`035GooOol01Goo00DD aGooOomooc6<00Eoo`04IcUoogooGooOol02Woo00GooOol017oo00Goo5GooOol01goo000aOol2BU83Ool3BU8>Ool2@03Ool2IcT>Ool3A=oo`A1oo`03Goo00=:DPQoo`03IcUoogoo00Qoo`Goo00Yo o`03IcUoogoo00Qoo`00Ogoo0S6<27oo00GooOol01Woo0VLi2goo0021Ool00c6AEoo`IW>@ioo`00ogoo87oo003oOolPOol00?moob1oo`00ogoo87oo003oOolPOol00?moob1oo`00 ogoo87oo003oOolPOol00?moob1oo`00ogoo87oo003oOolPOol00001\ \>"], ImageRangeCache->{{{0, 286.938}, {221.438, 0}} -> {-0.256057, -0.193192, 0.0366356, 0.0366356}, {{6.9375, 32}, {216.125, 200.063}} -> {-0.272582, -0.993001, 0.168094, 0.168094}, {{34.5, 59.5625}, { 216.125, 200.063}} -> {-4.90568, -0.993001, 0.168094, 0.168094}, {{62.0625, 87.125}, {216.125, 200.063}} -> {-9.53878, -0.993001, 0.168094, 0.168094}, {{89.625, 114.625}, {216.125, 200.063}} -> {-14.1666, -0.993001, 0.168094, 0.168094}, {{117.125, 142.188}, {216.125, 200.063}} -> {-18.7945, -0.993001, 0.168094, 0.168094}, {{144.688, 169.75}, {216.125, 200.063}} -> {-23.4276, -0.993001, 0.168094, 0.168094}, {{172.25, 197.25}, {216.125, 200.063}} -> {-28.0554, -0.993001, 0.168094, 0.168094}, {{199.813, 224.813}, {216.125, 200.063}} -> {-32.6885, -0.993001, 0.168094, 0.168094}, {{227.313, 252.375}, {216.125, 200.063}} -> {-37.3164, -0.993001, 0.168094, 0.168094}, {{254.875, 279.938}, {216.125, 200.063}} -> {-41.9495, -0.993001, 0.168094, 0.168094}, {{6.9375, 32}, { 198.438, 182.313}} -> {-0.262593, -3.95548, 0.167581, 0.167581}, {{34.5, 59.5625}, {198.438, 182.313}} -> {-4.88155, -3.95548, 0.167581, 0.167581}, {{62.0625, 87.125}, {198.438, 182.313}} -> {-9.50051, -3.95548, 0.167581, 0.167581}, {{89.625, 114.625}, {198.438, 182.313}} -> {-14.157, -3.9685, 0.168, 0.168}, {{117.125, 142.188}, { 198.438, 182.313}} -> {-18.7279, -3.95548, 0.167581, 0.167581}, {{144.688, 169.75}, {198.438, 182.313}} -> {-23.3469, -3.95548, 0.167581, 0.167581}, {{ 172.25, 197.25}, {198.438, 182.313}} -> {-28.038, -3.9685, 0.168, 0.168}, {{ 199.813, 224.813}, {198.438, 182.313}} -> {-32.6685, -3.9685, 0.168, 0.168}, {{227.313, 252.375}, {198.438, 182.313}} -> {-37.1933, -3.95548, 0.167581, 0.167581}, {{254.875, 279.938}, {198.438, 182.313}} -> {-41.8123, -3.95548, 0.167581, 0.167581}, {{6.9375, 32}, { 180.688, 164.625}} -> {-0.272582, -6.94984, 0.168094, 0.168094}, {{34.5, 59.5625}, {180.688, 164.625}} -> {-4.90568, -6.94984, 0.168094, 0.168094}, {{62.0625, 87.125}, {180.688, 164.625}} -> {-9.53878, -6.94984, 0.168094, 0.168094}, {{89.625, 114.625}, {180.688, 164.625}} -> {-14.1666, -6.94984, 0.168094, 0.168094}, {{117.125, 142.188}, {180.688, 164.625}} -> {-18.7945, -6.94984, 0.168094, 0.168094}, {{144.688, 169.75}, {180.688, 164.625}} -> {-23.4276, -6.94984, 0.168094, 0.168094}, {{172.25, 197.25}, {180.688, 164.625}} -> {-28.0554, -6.94984, 0.168094, 0.168094}, {{199.813, 224.813}, {180.688, 164.625}} -> {-32.6885, -6.94984, 0.168094, 0.168094}, {{227.313, 252.375}, {180.688, 164.625}} -> {-37.3164, -6.94984, 0.168094, 0.168094}, {{254.875, 279.938}, {180.688, 164.625}} -> {-41.9495, -6.94984, 0.168094, 0.168094}, {{6.9375, 32}, {163, 146.938}} -> {-0.272582, -9.92301, 0.168094, 0.168094}, {{34.5, 59.5625}, { 163, 146.938}} -> {-4.90568, -9.92301, 0.168094, 0.168094}, {{62.0625, 87.125}, {163, 146.938}} -> {-9.53878, -9.92301, 0.168094, 0.168094}, {{ 89.625, 114.625}, {163, 146.938}} -> {-14.1666, -9.92301, 0.168094, 0.168094}, {{117.125, 142.188}, {163, 146.938}} -> {-18.7945, -9.92301, 0.168094, 0.168094}, {{144.688, 169.75}, {163, 146.938}} -> {-23.4276, -9.92301, 0.168094, 0.168094}, {{172.25, 197.25}, { 163, 146.938}} -> {-28.0554, -9.92301, 0.168094, 0.168094}, {{199.813, 224.813}, {163, 146.938}} -> {-32.6885, -9.92301, 0.168094, 0.168094}, {{ 227.313, 252.375}, {163, 146.938}} -> {-37.3164, -9.92301, 0.168094, 0.168094}, {{254.875, 279.938}, {163, 146.938}} -> {-41.9495, -9.92301, 0.168094, 0.168094}, {{6.9375, 32}, {145.313, 129.188}} -> {-0.262593, -12.8582, 0.167581, 0.167581}, {{34.5, 59.5625}, { 145.313, 129.188}} -> {-4.88155, -12.8582, 0.167581, 0.167581}, {{62.0625, 87.125}, {145.313, 129.188}} -> {-9.50051, -12.8582, 0.167581, 0.167581}, {{ 89.625, 114.625}, {145.313, 129.188}} -> {-14.157, -12.8935, 0.168, 0.168}, {{117.125, 142.188}, {145.313, 129.188}} -> {-18.7279, -12.8582, 0.167581, 0.167581}, {{144.688, 169.75}, {145.313, 129.188}} -> {-23.3469, -12.8582, 0.167581, 0.167581}, {{172.25, 197.25}, { 145.313, 129.188}} -> {-28.038, -12.8935, 0.168, 0.168}, {{199.813, 224.813}, {145.313, 129.188}} -> {-32.6685, -12.8935, 0.168, 0.168}, {{ 227.313, 252.375}, {145.313, 129.188}} -> {-37.1933, -12.8582, 0.167581, 0.167581}, {{254.875, 279.938}, {145.313, 129.188}} -> {-41.8123, -12.8582, 0.167581, 0.167581}, {{6.9375, 32}, {127.563, 111.5}} -> {-0.272582, -15.8799, 0.168094, 0.168094}, {{34.5, 59.5625}, { 127.563, 111.5}} -> {-4.90568, -15.8799, 0.168094, 0.168094}, {{62.0625, 87.125}, {127.563, 111.5}} -> {-9.53878, -15.8799, 0.168094, 0.168094}, {{ 89.625, 114.625}, {127.563, 111.5}} -> {-14.1666, -15.8799, 0.168094, 0.168094}, {{117.125, 142.188}, {127.563, 111.5}} -> {-18.7945, -15.8799, 0.168094, 0.168094}, {{144.688, 169.75}, {127.563, 111.5}} -> {-23.4276, -15.8799, 0.168094, 0.168094}, {{172.25, 197.25}, { 127.563, 111.5}} -> {-28.0554, -15.8799, 0.168094, 0.168094}, {{199.813, 224.813}, {127.563, 111.5}} -> {-32.6885, -15.8799, 0.168094, 0.168094}, {{ 227.313, 252.375}, {127.563, 111.5}} -> {-37.3164, -15.8799, 0.168094, 0.168094}, {{254.875, 279.938}, {127.563, 111.5}} -> {-41.9495, -15.8799, 0.168094, 0.168094}, {{6.9375, 32}, {109.875, 93.8125}} -> {-0.272582, -18.853, 0.168094, 0.168094}, {{34.5, 59.5625}, { 109.875, 93.8125}} -> {-4.90568, -18.853, 0.168094, 0.168094}, {{62.0625, 87.125}, {109.875, 93.8125}} -> {-9.53878, -18.853, 0.168094, 0.168094}, {{ 89.625, 114.625}, {109.875, 93.8125}} -> {-14.1666, -18.853, 0.168094, 0.168094}, {{117.125, 142.188}, {109.875, 93.8125}} -> {-18.7945, -18.853, 0.168094, 0.168094}, {{144.688, 169.75}, {109.875, 93.8125}} -> {-23.4276, -18.853, 0.168094, 0.168094}, {{172.25, 197.25}, { 109.875, 93.8125}} -> {-28.0554, -18.853, 0.168094, 0.168094}, {{199.813, 224.813}, {109.875, 93.8125}} -> {-32.6885, -18.853, 0.168094, 0.168094}, {{ 227.313, 252.375}, {109.875, 93.8125}} -> {-37.3164, -18.853, 0.168094, 0.168094}, {{254.875, 279.938}, {109.875, 93.8125}} -> {-41.9495, -18.853, 0.168094, 0.168094}, {{6.9375, 32}, {92.1875, 76.0625}} -> {-0.262593, -21.761, 0.167581, 0.167581}, {{34.5, 59.5625}, { 92.1875, 76.0625}} -> {-4.88155, -21.761, 0.167581, 0.167581}, {{62.0625, 87.125}, {92.1875, 76.0625}} -> {-9.50051, -21.761, 0.167581, 0.167581}, {{ 89.625, 114.625}, {92.1875, 76.0625}} -> {-14.157, -21.8185, 0.168, 0.168}, {{117.125, 142.188}, {92.1875, 76.0625}} -> {-18.7279, -21.761, 0.167581, 0.167581}, {{144.688, 169.75}, {92.1875, 76.0625}} -> {-23.3469, -21.761, 0.167581, 0.167581}, {{172.25, 197.25}, { 92.1875, 76.0625}} -> {-28.038, -21.8185, 0.168, 0.168}, {{199.813, 224.813}, {92.1875, 76.0625}} -> {-32.6685, -21.8185, 0.168, 0.168}, {{ 227.313, 252.375}, {92.1875, 76.0625}} -> {-37.1933, -21.761, 0.167581, 0.167581}, {{254.875, 279.938}, {92.1875, 76.0625}} -> {-41.8123, -21.761, 0.167581, 0.167581}, {{6.9375, 32}, {74.4375, 58.375}} -> {-0.272582, -24.8099, 0.168094, 0.168094}, {{34.5, 59.5625}, { 74.4375, 58.375}} -> {-4.90568, -24.8099, 0.168094, 0.168094}, {{62.0625, 87.125}, {74.4375, 58.375}} -> {-9.53878, -24.8099, 0.168094, 0.168094}, {{ 89.625, 114.625}, {74.4375, 58.375}} -> {-14.1666, -24.8099, 0.168094, 0.168094}, {{117.125, 142.188}, {74.4375, 58.375}} -> {-18.7945, -24.8099, 0.168094, 0.168094}, {{144.688, 169.75}, {74.4375, 58.375}} -> {-23.4276, -24.8099, 0.168094, 0.168094}, {{172.25, 197.25}, { 74.4375, 58.375}} -> {-28.0554, -24.8099, 0.168094, 0.168094}, {{199.813, 224.813}, {74.4375, 58.375}} -> {-32.6885, -24.8099, 0.168094, 0.168094}, {{ 227.313, 252.375}, {74.4375, 58.375}} -> {-37.3164, -24.8099, 0.168094, 0.168094}, {{254.875, 279.938}, {74.4375, 58.375}} -> {-41.9495, -24.8099, 0.168094, 0.168094}, {{6.9375, 32}, {56.75, 40.6875}} -> {-0.272582, -27.783, 0.168094, 0.168094}, {{34.5, 59.5625}, { 56.75, 40.6875}} -> {-4.90568, -27.783, 0.168094, 0.168094}, {{62.0625, 87.125}, {56.75, 40.6875}} -> {-9.53878, -27.783, 0.168094, 0.168094}, {{ 89.625, 114.625}, {56.75, 40.6875}} -> {-14.1666, -27.783, 0.168094, 0.168094}, {{117.125, 142.188}, {56.75, 40.6875}} -> {-18.7945, -27.783, 0.168094, 0.168094}, {{144.688, 169.75}, {56.75, 40.6875}} -> {-23.4276, -27.783, 0.168094, 0.168094}, {{172.25, 197.25}, { 56.75, 40.6875}} -> {-28.0554, -27.783, 0.168094, 0.168094}, {{199.813, 224.813}, {56.75, 40.6875}} -> {-32.6885, -27.783, 0.168094, 0.168094}, {{ 227.313, 252.375}, {56.75, 40.6875}} -> {-37.3164, -27.783, 0.168094, 0.168094}, {{254.875, 279.938}, {56.75, 40.6875}} -> {-41.9495, -27.783, 0.168094, 0.168094}, {{6.9375, 32}, {39.0625, 22.9375}} -> {-0.262593, -30.6637, 0.167581, 0.167581}, {{34.5, 59.5625}, { 39.0625, 22.9375}} -> {-4.88155, -30.6637, 0.167581, 0.167581}, {{62.0625, 87.125}, {39.0625, 22.9375}} -> {-9.50051, -30.6637, 0.167581, 0.167581}, {{ 89.625, 114.625}, {39.0625, 22.9375}} -> {-14.157, -30.7435, 0.168, 0.168}, {{117.125, 142.188}, {39.0625, 22.9375}} -> {-18.7279, -30.6637, 0.167581, 0.167581}, {{144.688, 169.75}, {39.0625, 22.9375}} -> {-23.3469, -30.6637, 0.167581, 0.167581}, {{172.25, 197.25}, { 39.0625, 22.9375}} -> {-28.038, -30.7435, 0.168, 0.168}, {{199.813, 224.813}, {39.0625, 22.9375}} -> {-32.6685, -30.7435, 0.168, 0.168}, {{ 227.313, 252.375}, {39.0625, 22.9375}} -> {-37.1933, -30.6637, 0.167581, 0.167581}, {{254.875, 279.938}, {39.0625, 22.9375}} -> {-41.8123, -30.6637, 0.167581, 0.167581}, {{6.9375, 32}, {21.3125, 5.25}} -> {-0.272582, -33.7399, 0.168094, 0.168094}, {{34.5, 59.5625}, { 21.3125, 5.25}} -> {-4.90568, -33.7399, 0.168094, 0.168094}, {{62.0625, 87.125}, {21.3125, 5.25}} -> {-9.53878, -33.7399, 0.168094, 0.168094}, {{ 89.625, 114.625}, {21.3125, 5.25}} -> {-14.1666, -33.7399, 0.168094, 0.168094}, {{117.125, 142.188}, {21.3125, 5.25}} -> {-18.7945, -33.7399, 0.168094, 0.168094}, {{144.688, 169.75}, {21.3125, 5.25}} -> {-23.4276, -33.7399, 0.168094, 0.168094}, {{172.25, 197.25}, { 21.3125, 5.25}} -> {-28.0554, -33.7399, 0.168094, 0.168094}, {{199.813, 224.813}, {21.3125, 5.25}} -> {-32.6885, -33.7399, 0.168094, 0.168094}, {{ 227.313, 252.375}, {21.3125, 5.25}} -> {-37.3164, -33.7399, 0.168094, 0.168094}, {{254.875, 279.938}, {21.3125, 5.25}} -> {-41.9495, -33.7399, 0.168094, 0.168094}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Do-it-yourself permutations", "Section"], Cell[TextData[{ "A useful goal when programming combinatorial functions is to devise a \ method for generating results recursively, that is, computing results for \ case ", StyleBox["k", FontSlant->"Italic"], " using the results for case ", Cell[BoxData[ \(TraditionalForm\`k - 1\)]], ". While it is always possible to generate a (possibly huge) list of \ candidate sets and remove those not meeting our criteria, it is often \ inefficent and uninstructive. (However, the following section contains an \ example of this technique.)" }], "Text"], Cell[TextData[{ "For example, the relationship ", Cell[BoxData[ \(TraditionalForm \`\(n!\)\[InvisibleSpace] = n\[Times]\(\((n - 1)\)!\)\)]], " suggests that a procedure may exist for generating permutations of the \ numbers 1 through ", StyleBox["n", FontSlant->"Italic"], " using the permutations of the numbers 1 through ", Cell[BoxData[ \(TraditionalForm\`n - 1\)]], "." }], "Text"], Cell[TextData[{ "There are two permutations of the list ", Cell[BoxData[ \(TraditionalForm\`{1, 2}\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Permutations[{1, 2}]\)], "Input"], Cell[BoxData[ \({{1, 2}, {2, 1}}\)], "Output"] }, Open ]], Cell[TextData[{ "And there are six permutations of the list ", Cell[BoxData[ \(TraditionalForm\`{1, 2, 3}\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Permutations[{1, 2, 3}]\)], "Input"], Cell[BoxData[ \({{1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}}\)], "Output"] }, Open ]], Cell[TextData[{ "A bit of experimentation shows that inserting the number 3 into every \ possible location in the permutation ", Cell[BoxData[ \(TraditionalForm\`{1, 2}\)]], " leads to the lists ", Cell[BoxData[ \(TraditionalForm\`{1, 2, 3}\)]], ", ", Cell[BoxData[ \(TraditionalForm\`{1, 3, 2}\)]], ", and ", Cell[BoxData[ \(TraditionalForm\`{3, 1, 2}\)]], ", and inserting 3 into ", Cell[BoxData[ \(TraditionalForm\`{2, 1}\)]], " gives ", Cell[BoxData[ \(TraditionalForm\`{2, 1, 3}\)]], ", ", Cell[BoxData[ \(TraditionalForm\`{2, 3, 1}\)]], ", and ", Cell[BoxData[ \(TraditionalForm\`{3, 2, 1}\)]], ". As we can verify, this process generates a complete list of permutations \ of ", StyleBox["n", FontSlant->"Italic"], " elements, based on a complete list of permutations of ", Cell[BoxData[ \(TraditionalForm\`n - 1\)]], " elements." }], "Text"], Cell[TextData[{ StyleBox["ReplaceList", "Input"], " is a programming function new in ", StyleBox["Mathematica", FontSlant->"Italic"], " 3. ", StyleBox["ReplaceList", "Input"], " takes as arguments an expression and a list of transformation rules, and \ returns all possible results of transforming the expression. Nontrivial \ results arise when the transformation rules include double- or triple-blank \ patterns, which respectively match one or more, or zero or more, elements." }], "Text"], Cell["\<\ The following example uses a list of expressions matched with a \ sequence of two triple-blank patterns and returns the matched sequences with \ a new element inserted between them; the result is a list containing the \ original list with the new element inserted in each possible location.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(ReplaceList[{old, old, old}, {a___, b___} \[Rule] {a, NEW, b}]\)], "Input"], Cell[BoxData[ \({{NEW, old, old, old}, {old, NEW, old, old}, {old, old, NEW, old}, { old, old, old, NEW}}\)], "Output"] }, Open ]], Cell[TextData[{ "In general, a list with ", StyleBox["n", FontSlant->"Italic"], " elements has ", Cell[BoxData[ \(TraditionalForm\`n + 1\)]], " locations for a new element." }], "Text"], Cell[TextData[{ "The following definitions generate a list of all possible permutations of \ the numbers 1 through ", StyleBox["n", FontSlant->"Italic"], ", using the list of permutations of the numbers 1 through ", Cell[BoxData[ \(TraditionalForm\`n - 1\)]], "; the elementary, or starting, case is the empty list, which represents a \ complete list of permutations of a list with zero elements." }], "Text"], Cell[BoxData[ \(\(PermutationRule[n_] = {a___, b___} \[Rule] {a, n, b}; \)\)], "Input"], Cell[BoxData[ \(\(PermutationN[0] = {{}}; \)\)], "Input"], Cell[TextData[{ "Defining the recursive step using the form ", StyleBox[ "f[x_]\[ThinSpace]:=\[ThinSpace]f[x]\[ThinSpace]=\[ThinSpace]\ \[CenterEllipsis]", "Input"], " allows us to cache intermediate values, which speeds up subsequent \ calculations." }], "Text"], Cell[BoxData[ \(PermutationN[n_Integer?Positive] := \(PermutationN[n] = \n\t\t Flatten[Map[ReplaceList[#, PermutationRule[n]]&, PermutationN[n - 1]], 1]\)\)], "Input"], Cell["Here are some examples.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(PermutationN[2]\)], "Input"], Cell[BoxData[ \({{2, 1}, {1, 2}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(PermutationN[4]\)], "Input"], Cell[BoxData[ \({{4, 3, 2, 1}, {3, 4, 2, 1}, {3, 2, 4, 1}, {3, 2, 1, 4}, {4, 2, 3, 1}, { 2, 4, 3, 1}, {2, 3, 4, 1}, {2, 3, 1, 4}, {4, 2, 1, 3}, {2, 4, 1, 3}, { 2, 1, 4, 3}, {2, 1, 3, 4}, {4, 3, 1, 2}, {3, 4, 1, 2}, {3, 1, 4, 2}, { 3, 1, 2, 4}, {4, 1, 3, 2}, {1, 4, 3, 2}, {1, 3, 4, 2}, {1, 3, 2, 4}, { 4, 1, 2, 3}, {1, 4, 2, 3}, {1, 2, 4, 3}, {1, 2, 3, 4}}\)], "Output"] }, Open ]], Cell[TextData[{ "As an informal check of our results, we make certain the function returns \ the same results as the built-in ", StyleBox["Permutations", "Input"], " function." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Sort[%] == Permutations[{1, 2, 3, 4}]\)], "Input"], Cell[BoxData[ \(True\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Derangements", "Section"], Cell[TextData[{ "One special type of permutation is the ", StyleBox["derangement", FontSlant->"Italic"], ", which is a permutation that leaves no element in its original position. \ Assuming that we'll permute only lists of consecutive integers 1 through ", StyleBox["n", FontSlant->"Italic"], ", the following predicate function detects derangements by subtracting the \ candidate permutation from the identity permutation, and checking to see that \ the result is free of any zeros." }], "Text"], Cell[BoxData[ \(DerangementQ[perm_List] := FreeQ[Range[Length[perm]] - perm, 0]\)], "Input"], Cell[TextData[{ "The following permutation is a derangement of ", Cell[BoxData[ \(TraditionalForm\`{1, 2, 3}\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(DerangementQ[{2, 3, 1}]\)], "Input"], Cell[BoxData[ \(True\)], "Output"] }, Open ]], Cell[TextData[{ "The permutation ", Cell[BoxData[ \(TraditionalForm\`{2, 1, 3}\)]], " leaves 3 in its original position, so it is not a derangement of ", Cell[BoxData[ \(TraditionalForm\`{1, 2, 3}\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(DerangementQ[{2, 1, 3}]\)], "Input"], Cell[BoxData[ \(False\)], "Output"] }, Open ]], Cell["\<\ We can then enumerate the derangements of a list by enumerating the \ permutations and removing those that are not derangements.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Select[PermutationN[3], DerangementQ]\)], "Input"], Cell[BoxData[ \({{2, 3, 1}, {3, 1, 2}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Select[PermutationN[4], DerangementQ]\)], "Input"], Cell[BoxData[ \({{4, 3, 2, 1}, {3, 4, 2, 1}, {2, 3, 4, 1}, {2, 4, 1, 3}, {2, 1, 4, 3}, { 4, 3, 1, 2}, {3, 4, 1, 2}, {3, 1, 4, 2}, {4, 1, 2, 3}}\)], "Output"] }, Open ]], Cell[TextData[{ "At this point, we might as well define a function ", StyleBox["Derangements", "Input"], ". (Note that this function does not generate the lists of derangements \ recursively; such a recursion is complicated enough to negate its educational \ benefits.) " }], "Text"], Cell[BoxData[ \(Derangements[n_] := Select[PermutationN[n], DerangementQ]\)], "Input"], Cell[TextData[{ "We can then modify the body of ", StyleBox["PermutationDiagrams", "Input"], " to visualize the list of derangements." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(With[{allpairs = Map[Partition[#, 2, 1]&, Derangements[4]]}, \(Show@\(GraphicsArray@Partition[#, 3]\)&\)@ Map[Show[Graphics[#], DisplayFunction \[Rule] Identity, PlotRange \[Rule] {Automatic, {\(-0.1\), 2.1}}]&, Map[MapIndexed[{GrayLevel[First[#2]/4], #}&, #]&, Map[Semicircle, allpairs, {2}]]]]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .69841 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.31746 0.0166289 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.0166289 0.321429 0.22449 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .81746 .03175 .15873 0 180 arc s .5 g newpath .5 .03175 .47619 0 180 arc s .75 g newpath .18254 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.35119 0.0166289 0.64881 0.22449 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .34127 .03175 .31746 0 180 arc s .5 g newpath .5 .03175 .47619 0 180 arc s .75 g newpath .65873 .03175 .31746 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.678571 0.0166289 0.97619 0.22449 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .5 .03175 .47619 0 180 arc s .5 g newpath .18254 .03175 .15873 0 180 arc s .75 g newpath .5 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.245276 0.321429 0.453137 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .65873 .03175 .31746 0 180 arc s .5 g newpath .5 .03175 .47619 0 180 arc s .75 g newpath .34127 .03175 .31746 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.35119 0.245276 0.64881 0.453137 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .18254 .03175 .15873 0 180 arc s .5 g newpath .5 .03175 .47619 0 180 arc s .75 g newpath .81746 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.678571 0.245276 0.97619 0.453137 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .81746 .03175 .15873 0 180 arc s .5 g newpath .34127 .03175 .31746 0 180 arc s .75 g newpath .18254 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.473923 0.321429 0.681784 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .81746 .03175 .15873 0 180 arc s .5 g newpath .5 .03175 .15873 0 180 arc s .75 g newpath .18254 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.35119 0.473923 0.64881 0.681784 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .81746 .03175 .15873 0 180 arc s .5 g newpath .65873 .03175 .31746 0 180 arc s .75 g newpath .18254 .03175 .15873 0 180 arc s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.678571 0.473923 0.97619 0.681784 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations -0.293651 0.31746 0.031746 0.31746 [ [ 0 0 0 0 ] [ 1 .69841 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .69841 L 0 .69841 L closepath clip newpath .25 g .5 Mabswid newpath .5 .03175 .15873 0 180 arc s .5 g newpath .81746 .03175 .15873 0 180 arc s .75 g newpath .5 .03175 .47619 0 180 arc s MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{168.75, 117.813}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgMoogoo00aoo`03?Nmoogoo00Eoo`03?Nmoogoo00eoo`03G_Moogoo00aoo`037>Moogoo 00eoo`03G_Moogoo00Eoo`03?Nmoogoo00aoo`03G_Moogoo00eoo`03G_Moogoo00eoo`037>Moogoo 00=oo`001Goo00=NmgooOol03Goo00=NmgooOol03Goo00 Ool00acWOomoo`0Ool00acWOomoo`03 Ool000Eoo`03?NmNmgoo00]oo`03G_Moogoo011oo`037>Moogoo00Yoo`037>Lmkgoo00Ioo`03?Nmo ogoo00eoo`03G_Moogoo00aoo`037>Moogoo00eoo`03G_Moogoo00Eoo`037>Lmkgoo00]oo`04?Nmo ogooG_LMoogoo00Yoo`037>Lmkgoo00Ioo`03?NlLigoo00ioo`03G_Moogoo00Yoo`037>Moogoo00eo o`03G_Lmkgoo00Ioo`037>Lmkgoo00]oo`04?NmoogooG_L;Ool00ekgOomoo`0>Ool00acWOomoo`04 Ool000Ioo`03?NmNmekg00Uoo`03G_Moogoo019oo`037>Moogoo00Moo`8Li`03?Nmoogoo00Moo`03 ?Nmoogoo00eoo`03G_Moogoo00Yoo`037>Moogoo00eoo`03G_Moogoo00Ioo`037>Moocg_00Uoo`8m k`Aoo`03G_Moogoo00Moo`9Nma1oo`037>Moogoo00Aoo`001Woo00L4Ool00cg_Oomoo`08Ool00cg_7>Moo`0>Ool00ekgOomoo`08 Ool00acWOomoo`0=Ool00ekgOomoo`08Ool00acWOomoo`02Ool3?Nl=Ool3G_LDOol00acWOomoo`05 Ool000Moo`03?Nmoogoo02Qoo`03?Nmoogoo00Qoo`03?NlLigoo00ioo`03G_Moogoo00Qoo`037>Mo ogoo00aoo`03G_Lmkgoo00Uoo`037>Moogoo02Uoo`037>Moogoo00Eoo`0027oo00L>Ool015kgOomoogoo0QcW 3Woo00=Nmgoo?Nl03Woo00L03goo00ANmgooOolmk`ioo`037>Moogoo02Eoo`03 7>Moogoo00Moo`002Woo00MNmekg 00eoo`9Nm`9oo`03?Nmoogoo00ioo`037>Moogoo02=oo`037>Moogoo00Qoo`002Woo00MoogooOol2G_L9Ool2G_L4Ool00cg_Oomo o`0?Ool00acWOomoo`0QOol00acWOomoo`09Ool000]oo`03?Nmoogoo021oo`03?Nmoogoo015oo`03 ?Nmoogoo009oo`XLi`Ioo`UNm`Eoo`03?Nmoogoo015oo`037>Moogoo01moo`037>Moogoo00Yoo`00 37oo00LM Ool27>L=Ool000moo`03?Nmoogoo01Uoo`03?Nmoogoo01Moo`03?Nmoogoo01Uoo`03?Nmoogoo01Qo o`037>Moogoo01Uoo`037>Moogoo00eoo`003goo00LEOol27>LAOol001=oo`8mka1oo`LJOol00:Qoo`00Z7oo002XOol00:Qoo`00Z7oo002XOol00:Qoo`00Z7oo002XOol00:Qoo`00 Z7oo002XOol00:Qoo`001Goo00=NmgooOol03Goo00Moogoo00aoo`03G_Moogoo00eoo`03?Nmoogoo 00Eoo`03?Nmoogoo00aoo`037>Moogoo00eoo`03G_Moogoo00eoo`03G_Moogoo00Aoo`03?NmNmgoo 00eoo`03G_Moogoo00eoo`03?Nmoogoo00eoo`037>Moogoo00=oo`001Goo00=NmgooOol03Goo00Moo`0;Ool00acWOomoo`0@Ool00ekgOomoo`0:Ool00ekg?Nmoo`06Ool00cg_G_Moo`0; Ool00ekgOomoo`0>Ool00cg_7>Moo`0;Ool00acWOomoo`05Ool000Eoo`03?NmNmgoo00ioo`037>Mo ogoo00Yoo`03G_Moogoo00eoo`037>Lmkgoo00Ioo`03?NlLigoo00]oo`037>Moogoo011oo`03G_Mo ogoo00Uoo`03G_Moocg_00Qoo`03G_Moogoo00Yoo`03G_Moogoo00eoo`04?Nmoogoo7>L;Ool00acW Oomoo`05Ool000Ioo`03G_Moogoo00eoo`037>Moogoo00Yoo`03G_Moogoo00eoo`03?Nmoogoo00Mo o`03?NlLigoo00Uoo`037>Moogoo019oo`03G_Moogoo00Qoo`03G_Lmkgoo00Qoo`03?NmNmgoo00Uo o`03G_Moogoo00ioo`04?Nmoogoo7>L:Ool00acWOomoo`06Ool000Ioo`03?NmNmgoo00eoo`037>Mo ogoo00Yoo`03G_Moogoo00eoo`03?Nmoogoo00Moo`04?NmooacW7>L7Ool00acWOomoo`0DOol00ekg Oomoo`05Ool2G_L00goo?Nmoo`08Ool00cg_OomNm`07Ool2G_L@Ool00cg_Oomoo`02Ool27>L7Ool0 0acWOomoo`07Ool000Moo`03G_Moogoo00eoo`037>Moogoo00Qoo`03G_Moogoo00eoo`03?Nmoogoo 00Qoo`04?NmoogooOol77>LHOol7G_L2Ool00cg_Oomoo`09Ool00cg_OomNm`06G_LBOol00cg_Oomo o`04Ool77>L:Ool000Moo`03?NmNmgoo00eoo`037>Moogoo00Qoo`03G_Moogoo00eoo`03?Nmoogoo 00Qoo`03?Nmoogoo02Uoo`03?Nmoogoo00Uoo`03?Nmoogoo01Moo`03?Nmoogoo01Ioo`0027oo00Ool00acWOomoo`04 Ool00ekgOomoo`0=Ool00acW?Nmoo`0;Ool00cg_Oomoo`0WOol00cg_Oomoo`0MNmgoo00ioo`047>Moogoo?Nl?Ool00cg_Oomoo`0TOol00cg_Oomoo`0?Ool00cg_Oomo o`0?Ool00cg_Oomoo`0JOol000Yoo`03?Nmoogoo009Nm`eoo`03G_LLigoo00eoo`047>Moogoo?NlA Ool00cg_Oomoo`0ROol00cg_Oomoo`0AOol2?Nl=Ool2?NlMOol000Yoo`03?Nmoogoo009oo`9Nm`Uo o`9Nm`9oo`8Li`Yoo`8Li`=oo`03?Nmoogoo00moo`03?Nmoogoo029oo`03?Nmoogoo01=oo`8mk`Uo o`8mkamoo`002goo00Moogoo00Eoo`03G_Moogoo00aoo`03G_Moogoo00eoo`037>Moogoo00eo o`03?Nmoogoo00Aoo`03G_Moogoo00eoo`037>Moogoo00eoo`03?Nmoogoo00eoo`03G_Moogoo00=o o`001Goo00=NmgooOol03Goo00=NmgooOol037oo00Moo`0=Ool00acWOomoo`05Ool00ekgOomoo`0Ool00acWOomoo`0;Ool0 0acW?Nmoo`06Ool00ekgOomoo`0=Ool00acWOomoo`0;Ool00acWOolmk`0=Ool00cg_G_Moo`04Ool0 00Ioo`03G_Moogoo00]oo`03G_Lmkgoo00eoo`03?NlLigoo00eoo`037>Moogoo00Eoo`03G_Moogoo 00aoo`03G_Lmkgoo00ioo`037>Moogoo00]oo`037>Lmkgoo00Ioo`03G_Moogoo00eoo`037>Moogoo 00]oo`037>Moocg_00eoo`03G_Moogoo00Aoo`001goo00=NmgooOol02Goo00ANmgooOolmk`aoo`04 ?Nmoogoo7>LOol00acWOomoo`09Ool01AcWOomoogoo?Nl02goo00Ool00cg_Oomoo`0GOol00cg_Oomoo`09Ool00ekgOomo o`0YOol00ekgOomoo`05Ool004moo`03?Nmoogoo01Eoo`03?Nmoogoo00Yoo`03G_Moogoo02Uoo`03 G_Moogoo00Eoo`00Cgoo00"], ImageRangeCache->{{{0, 167.75}, {116.813, 0}} -> {-0.0796622, -0.0523811, 0.0188335, 0.0188335}, {{4.1875, 54}, {114, 79.25}} -> { 0.658102, -0.278057, 0.0633092, 0.0633092}, {{58.9375, 108.75}, {114, 79.25}} -> {-2.80808, -0.278057, 0.0633092, 0.0633092}, {{113.688, 163.5}, { 114, 79.25}} -> {-6.27425, -0.278057, 0.0633092, 0.0633092}, {{4.1875, 54}, {75.75, 41}} -> {0.658102, -2.69963, 0.0633092, 0.0633092}, {{58.9375, 108.75}, {75.75, 41}} -> {-2.80808, -2.69963, 0.0633092, 0.0633092}, {{ 113.688, 163.5}, {75.75, 41}} -> {-6.27425, -2.69963, 0.0633092, 0.0633092}, {{4.1875, 54}, {37.5, 2.75}} -> {0.658102, -5.12121, 0.0633092, 0.0633092}, {{58.9375, 108.75}, {37.5, 2.75}} -> {-2.80808, -5.12121, 0.0633092, 0.0633092}, {{113.688, 163.5}, {37.5, 2.75}} -> {-6.27425, -5.12121, 0.0633092, 0.0633092}}] }, Open ]], Cell["\<\ The diagrams aren't particularly interesting, though, since they \ don't really show how derangements leave no element in its original position; \ and so it's time to think of another approach.\ \>", "Text"], Cell[TextData[{ "Another way to represent the elements in a list is as indexed points \ equally spaced around the perimeter of a circle. Since this is a \ representation that we'll use several times, we define a function ", StyleBox["Poly", "Input"], " that generates such a list of coordinates." }], "Text"], Cell[BoxData[ \(Poly[n_] := \({Cos[#], Sin[#]}&\)/@Range[0, 2\ \[Pi], \(2\ \[Pi]\)\/n]\)], "Input"], Cell[TextData[{ "(Note that ", StyleBox["Poly", "Input"], " creates a list whose first and last elements are the same, which comes in \ handy when we're drawing polygons using the ", StyleBox["Line", "Input"], " graphics primitive; otherwise there would be an edge missing from the \ polygon, which gets to be a nuisance after you've had to correct for it a few \ times.)" }], "Text"], Cell[TextData[{ "Here we verify that ", StyleBox["Poly[5]", "Input"], " represents a regular pentagon." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[Graphics[Line[Poly[5]]]]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.05146 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.526463 0.525731 0.526463 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath 0 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{154.813, 162.75}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg7oo001DOol30009Ool00`00Oomoo`0gOol0051oo`@000eoo`03001oogoo03Ioo`00CGoo0`004Woo 00<007ooOol0=Goo001:Ool3000EOol00`00Oomoo`0eOol004Moo`<001Uoo`03001oogoo03Aoo`00 A7oo0`007Goo00<007ooOol0Woo1000:7oo00<007ooOol07oo001J Ool30002Ool00`00Oomoo`0hOol005eoo`8003]oo`00VWoo002JOol009Yoo`00\ \>"], ImageRangeCache->{{{0, 153.813}, {161.75, 0}} -> {-0.854242, -0.998747, 0.0123492, 0.0123492}}] }, Open ]], Cell[TextData[{ "We can then draw lines or arrows connecting the vertices corresponding to \ related elements in a list. For example, we might represent the relationship \ between the identity list ", Cell[BoxData[ \(TraditionalForm\`{1, 2, 3}\)]], " and its derangement ", Cell[BoxData[ \(TraditionalForm\`{3, 1, 2}\)]], " by drawing arrows connecting an element's position in the identity list \ to its position in the \ \[OpenCurlyDoubleQuote]deranged\[CloseCurlyDoubleQuote] list." }], "Text"], Cell[TextData[{ "First we load the package that defines the ", StyleBox["Arrow", "Input"], " graphics primitive, and make the arrowheads easier to see by giving new \ values to the ", StyleBox["HeadCenter", "Input"], " and ", StyleBox["HeadWidth", "Input"], " options." }], "Text"], Cell[BoxData[ \(\(Needs["\"]; \)\)], "Input"], Cell[BoxData[ \(\(SetOptions[Arrow, HeadCenter \[Rule] 1, HeadWidth \[Rule] 1]; \)\)], "Input"], Cell[TextData[{ "Here is our diagram for the derangement ", Cell[BoxData[ \(TraditionalForm\`{3, 1, 2}\)]], ", in which the arrows indicate that the element 3 moves to position\ \[NonBreakingSpace]1, element 1 moves to position 2, and element 2 moves to \ position 3. (In this and subsequent diagrams, the leftmost vertex in a \ polygon represents element 1, and the other elements are arranged \ counterclockwise around the center of the polygon.)" }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(tri = Poly[3]; Show[Graphics[{ Arrow[tri\[LeftDoubleBracket]3\[RightDoubleBracket], tri\[LeftDoubleBracket]1\[RightDoubleBracket]], Arrow[tri\[LeftDoubleBracket]1\[RightDoubleBracket], tri\[LeftDoubleBracket]2\[RightDoubleBracket]], Arrow[tri\[LeftDoubleBracket]2\[RightDoubleBracket], tri\[LeftDoubleBracket]3\[RightDoubleBracket]]}]]; \)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.1547 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.34127 0.634921 0.57735 0.634921 [ [ 0 0 0 0 ] [ 1 1.1547 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.1547 L 0 1.1547 L closepath clip newpath % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl 0. eq { 0 0 Mdot } { [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.05 0.025 moveto 0 0 lineto -0.05 -0.025 lineto fill -0.05 0.025 moveto 0 0 lineto -0.05 -0.025 lineto -0.05 0.025 lineto stroke } ifelse grestore } def % End of user PostScript 0 g .5 Mabswid .02381 .02749 m .97619 .57735 L s % Start of user PostScript -0.5 -0.866025 1. 0 MAarrowhead1 % End of user PostScript .97619 .57735 m .02381 1.12721 L s % Start of user PostScript 1. 0 -0.5 0.866025 MAarrowhead1 % End of user PostScript .02381 1.12721 m .02381 .02749 L s % Start of user PostScript -0.5 0.866025 -0.5 -0.866025 MAarrowhead1 % End of user PostScript % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{99.5625, 114.938}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg7oo0002Ool00`00Oomoo`0VOol00`00Oomoo`0eOol0009oo`03001oogoo02Moo`8003Eoo`000Woo 00<007ooOol0:Goo0P007oo0P00 97oo0002Ool00`00Oomoo`0jOol2000ROol0009oo`03001oogoo03aoo`80021oo`000Woo00<007oo Ool0?Woo00<007ooOol07Goo0002Ool00`00Oomoo`0oOol2000MOol0009oo`03001oogoo045oo`80 01]oo`000Woo00<007ooOol0@goo00<007ooOol067oo0002Ool00`00Oomoo`14Ool2000HOol0009o o`03001oogoo04Ioo`8001Ioo`000Woo00<007ooOol0B7oo0P0057oo0002Ool00`00Oomoo`1:Ool0 0`00Oomoo`0AOol0009oo`03001oogoo04]oo`80015oo`000Woo00<007ooOol0CGoo0P003goo0002 Ool00`00Oomoo`1?Ool00`00Oomoo`07oo0P0097oo0002Ool00`00Oomoo`0fOol2000V Ool0009oo`03001oogoo03Aoo`8002Qoo`000Woo00<007ooOol0Goo0002Ool00`00Oomoo`0QOol2000kOol0009o o`03001oogoo01moo`8003eoo`000Woo00<007ooOol07Woo00<007ooOol0?Goo0002Ool00`00Oomo o`0LOol20010Ool0009oo`03001oogoo01Yoo`80049oo`000Woo00<007ooOol067oo0P00A7oo0002 Ool00`00Oomoo`0GOol00`00Oomoo`14Ool0009oo`03001oogoo01Eoo`8004Moo`000Woo00<007oo Ool04goo0P00BGoo0002Ool00`00Oomoo`0BOol00`00Oomoo`19Ool0009oo`03001oogoo011oo`80 04aoo`000Woo00<007ooOol03Woo0P00CWoo0002Ool00`00Oomoo`0"], ImageRangeCache->{{{0, 98.5625}, {113.938, 0}} -> {-0.5375, -0.910343, 0.0159797, 0.0159797}}] }, Open ]], Cell["\<\ Here is a function that generates a graphics object for any \ derangement, additionally using a different color for each arrow.\ \>", "Text"], Cell[BoxData[ \(DerangementGraphic[L_List] := Module[{len = Length[L], thisPoly = Poly[Length[L]], endpoints}, endpoints = Transpose[{L, Range[len]}]; Graphics[ MapIndexed[{Hue[First[#2]/len], Arrow@@Part[thisPoly, #]}&, endpoints]]]\)], "Input"], Cell[TextData[{ "Here is our new picture for the list ", Cell[BoxData[ \(TraditionalForm\`{3, 1, 2}\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[DerangementGraphic[{3, 1, 2}]]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.1547 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.34127 0.634921 0.57735 0.634921 [ [ 0 0 0 0 ] [ 1 1.1547 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.1547 L 0 1.1547 L closepath clip newpath % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl 0. eq { 0 0 Mdot } { [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.05 0.025 moveto 0 0 lineto -0.05 -0.025 lineto fill -0.05 0.025 moveto 0 0 lineto -0.05 -0.025 lineto -0.05 0.025 lineto stroke } ifelse grestore } def % End of user PostScript 0 1 0 r .5 Mabswid .02381 .02749 m .97619 .57735 L s % Start of user PostScript -0.5 -0.866025 1. 0 MAarrowhead1 % End of user PostScript 0 0 1 r .97619 .57735 m .02381 1.12721 L s % Start of user PostScript 1. 0 -0.5 0.866025 MAarrowhead1 % End of user PostScript 1 0 0 r .02381 1.12721 m .02381 .02749 L s % Start of user PostScript -0.5 0.866025 -0.5 -0.866025 MAarrowhead1 % End of user PostScript % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{99.625, 115}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgGoo0002Ool00g`0Oomoo`0UOol00`?P Oomoo`0fOol0009oo`03O01oogoo02Ioo`83h3Ioo`000Woo00=l07ooOol0:7oo0P?P=7oo0002Ool0 0g`0Oomoo`0ZOol20n0bOol0009oo`03O01oogoo02aoo`030n1oogoo02moo`000Woo00=l07ooOol0 ;Goo0P?P;goo0002Ool00g`0Oomoo`0_Ool20n0]Ool0009oo`03O01oogoo035oo`83h2]oo`000Woo 00=l07ooOol07oo0P?P97oo0002Ool00g`0Oomoo`0jOol00`?POomoo`0Q Ool0009oo`03O01oogoo03]oo`83h25oo`000Woo00=l07ooOol0?Goo0P?P7goo0002Ool00g`0Oomo o`0oOol20n0MOol0009oo`03O01oogoo045oo`030n1oogoo01Yoo`000Woo00=l07ooOol0@Woo0P?P 6Woo0002Ool00g`0Oomoo`14Ool20n0HOol0009oo`03O01oogoo04Ioo`030n1oogoo01Eoo`000Woo 00=l07ooOol0Agoo0P?P5Goo0002Ool00g`0Oomoo`19Ool20n0COol0009oo`03O01oogoo04]oo`83 h15oo`000Woo00=l07ooOol0CGoo00<3h7ooOol03Woo0002Ool00g`0Oomoo`1>Ool20n0>Ool0009o o`03O01oogoo051oo`83h0aoo`000Woo00=l07ooOol0DWoo0P?P2Woo0002Ool00g`0Oomoo`1DOol0 1@?POomoogoo0n001Goo0002Ool00g`0Oomoo`1EOol50n04Ool0009oo`03O01oogoo05Ioo`D3h0=o o`000Woo00=l07ooOol0EWoo1@?P0goo0002Ool00g`0Oomoo`1EOol60n0101l1Ool1Ool0009oo`03 O01oogoo05Uoo`807`=oo`000Woo00=l07ooOol0Egoo0P0O1Goo0002Ool00g`0Oomoo`1FOol00`0O Oomoo`05Ool0009oo`03O01oogoo05Aoo`807`Qoo`000Woo00=l07ooOol0DWoo0P0O2Woo0002Ool0 0g`0Oomoo`1@Ool201l7oo0P0O 97oo0002Ool00g`0Oomoo`0gOol00`0OOomoo`0TOol0009oo`03O01oogoo03Eoo`807bMoo`000Woo 00=l07ooOol07oo0002Ool00g`0Oomoo`0ROol201ljOol0009oo`03O01oogoo025oo`0301moogoo03Yoo`000Woo 00=l07ooOol07goo0P0O?Goo0002Ool00g`0Oomoo`0MOol201loOol0009oo`03O01oogoo01]oo`80 7d5oo`000Woo00=l07ooOol06Woo00<07gooOol0@Goo0002Ool00g`0Oomoo`0HOol201m4Ool0009o o`03O01oogoo01Ioo`807dIoo`000Woo00=l07ooOol05Goo00<07gooOol0AWoo0002Ool00g`0Oomo o`0COol201m9Ool0009oo`03O01oogoo015oo`807d]oo`000Woo00=l07ooOol03goo0P0OCGoo0002 Ool00g`0Oomoo`0>Ool00`0OOomoo`1=Ool0009oo`03O01oogoo00aoo`807e1oo`000Woo00=l07oo Ool02Woo0P0ODWoo0002Ool00g`0Oomoo`09Ool00`0OOomoo`1BOol0009oo`03O01oogoo00Moo`80 7eEoo`000Woo00Al07ooOol07`Aoo`807eMoo`000Woo00=l07oo01l00P0O00=oo`0O01l0FGoo0002 Ool00g`0Ool07`0301mKOol0009oo`03O0007`0O00<07e]oo`000Woo00=l000O01l00`0OFgoo0002 Ool00g`001l07`1NOol006=oo`00Hgoo0000\ \>"], ImageRangeCache->{{{0, 98.625}, {114, 0}} -> {-0.5375, -0.910266, 0.0159696, 0.0159696}}] }, Open ]], Cell[TextData[{ "Here is a function that shows all the derangements for the list ", Cell[BoxData[ \(TraditionalForm\`{1, 2, \[Ellipsis], \ n}\)]], ". (It turns out that the number of derangements of a list satisfies the \ recurrence relation ", Cell[BoxData[ \(TraditionalForm \`D\_n = \((n - 1)\) \((D\_\(n - 1\) + D\_\(n - 2\))\)\)]], ", so we can safely partition the list of derangements into an array with \ rows ", Cell[BoxData[ \(TraditionalForm\`n - 1\)]], " elements wide.)" }], "Text"], Cell[BoxData[ \(ShowDerangementDiagrams[n_Integer /; n > 2] := Show[GraphicsArray[ Partition[Map[DerangementGraphic, Derangements[n]], n - 1]]]\)], "Input"], Cell[TextData[{ "Here are the derangements of ", Cell[BoxData[ \(TraditionalForm\`{1, 2, 3, 4}\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(ShowDerangementDiagrams[4]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.31746 0.0238095 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl 0. eq { 0 0 Mdot } { [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.05 0.025 moveto 0 0 lineto -0.05 -0.025 lineto fill -0.05 0.025 moveto 0 0 lineto -0.05 -0.025 lineto -0.05 0.025 lineto stroke } ifelse grestore } def % End of user PostScript % Start of sub-graphic p 0.0238095 0.0238095 0.321429 0.321429 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.47619 0.5 0.47619 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 1 0 r .5 Mabswid .02381 .5 m .97619 .5 L s % Start of user PostScript -1. 0 1. 0 MAarrowhead1 % End of user PostScript 0 1 1 r .5 .02381 m .5 .97619 L s % Start of user PostScript 0 -1. 0 1. MAarrowhead1 % End of user PostScript .5 0 1 r .97619 .5 m .02381 .5 L s % Start of user PostScript 1. 0 -1. 0 MAarrowhead1 % End of user PostScript 1 0 0 r .5 .97619 m .5 .02381 L s % Start of user PostScript 0 1. 0 -1. MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.35119 0.0238095 0.64881 0.321429 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.47619 0.5 0.47619 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 1 0 r .5 Mabswid .02381 .5 m .97619 .5 L s % Start of user PostScript -1. 0 1. 0 MAarrowhead1 % End of user PostScript 0 1 1 r .97619 .5 m .5 .97619 L s % Start of user PostScript 1. 0 0 1. MAarrowhead1 % End of user PostScript .5 0 1 r .5 .02381 m .02381 .5 L s % Start of user PostScript 0 -1. -1. 0 MAarrowhead1 % End of user PostScript 1 0 0 r .5 .97619 m .5 .02381 L s % Start of user PostScript 0 1. 0 -1. MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.678571 0.0238095 0.97619 0.321429 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.47619 0.5 0.47619 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 1 0 r .5 Mabswid .5 .02381 m .97619 .5 L s % Start of user PostScript 0 -1. 1. 0 MAarrowhead1 % End of user PostScript 0 1 1 r .97619 .5 m .5 .97619 L s % Start of user PostScript 1. 0 0 1. MAarrowhead1 % End of user PostScript .5 0 1 r .5 .97619 m .02381 .5 L s % Start of user PostScript 0 1. -1. 0 MAarrowhead1 % End of user PostScript 1 0 0 r .02381 .5 m .5 .02381 L s % Start of user PostScript -1. 0 0 -1. MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.35119 0.321429 0.64881 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.47619 0.5 0.47619 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 1 0 r .5 Mabswid .5 .97619 m .97619 .5 L s % Start of user PostScript 0 1. 1. 0 MAarrowhead1 % End of user PostScript 0 1 1 r .5 .02381 m .5 .97619 L s % Start of user PostScript 0 -1. 0 1. MAarrowhead1 % End of user PostScript .5 0 1 r .97619 .5 m .02381 .5 L s % Start of user PostScript 1. 0 -1. 0 MAarrowhead1 % End of user PostScript 1 0 0 r .02381 .5 m .5 .02381 L s % Start of user PostScript -1. 0 0 -1. MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.35119 0.35119 0.64881 0.64881 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.47619 0.5 0.47619 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 1 0 r .5 Mabswid .5 .97619 m .97619 .5 L s % Start of user PostScript 0 1. 1. 0 MAarrowhead1 % End of user PostScript 0 1 1 r .97619 .5 m .5 .97619 L s % Start of user PostScript 1. 0 0 1. MAarrowhead1 % End of user PostScript .5 0 1 r .5 .02381 m .02381 .5 L s % Start of user PostScript 0 -1. -1. 0 MAarrowhead1 % End of user PostScript 1 0 0 r .02381 .5 m .5 .02381 L s % Start of user PostScript -1. 0 0 -1. MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.678571 0.35119 0.97619 0.64881 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.47619 0.5 0.47619 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 1 0 r .5 Mabswid .5 .02381 m .97619 .5 L s % Start of user PostScript 0 -1. 1. 0 MAarrowhead1 % End of user PostScript 0 1 1 r .02381 .5 m .5 .97619 L s % Start of user PostScript -1. 0 0 1. MAarrowhead1 % End of user PostScript .5 0 1 r .97619 .5 m .02381 .5 L s % Start of user PostScript 1. 0 -1. 0 MAarrowhead1 % End of user PostScript 1 0 0 r .5 .97619 m .5 .02381 L s % Start of user PostScript 0 1. 0 -1. MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.678571 0.321429 0.97619 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.47619 0.5 0.47619 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 1 0 r .5 Mabswid .5 .02381 m .97619 .5 L s % Start of user PostScript 0 -1. 1. 0 MAarrowhead1 % End of user PostScript 0 1 1 r .02381 .5 m .5 .97619 L s % Start of user PostScript -1. 0 0 1. MAarrowhead1 % End of user PostScript .5 0 1 r .5 .97619 m .02381 .5 L s % Start of user PostScript 0 1. -1. 0 MAarrowhead1 % End of user PostScript 1 0 0 r .97619 .5 m .5 .02381 L s % Start of user PostScript 1. 0 0 -1. MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.35119 0.678571 0.64881 0.97619 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.47619 0.5 0.47619 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 1 0 r .5 Mabswid .02381 .5 m .97619 .5 L s % Start of user PostScript -1. 0 1. 0 MAarrowhead1 % End of user PostScript 0 1 1 r .5 .02381 m .5 .97619 L s % Start of user PostScript 0 -1. 0 1. MAarrowhead1 % End of user PostScript .5 0 1 r .5 .97619 m .02381 .5 L s % Start of user PostScript 0 1. -1. 0 MAarrowhead1 % End of user PostScript 1 0 0 r .97619 .5 m .5 .02381 L s % Start of user PostScript 1. 0 0 -1. MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.678571 0.678571 0.97619 0.97619 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.47619 0.5 0.47619 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 1 0 r .5 Mabswid .5 .97619 m .97619 .5 L s % Start of user PostScript 0 1. 1. 0 MAarrowhead1 % End of user PostScript 0 1 1 r .02381 .5 m .5 .97619 L s % Start of user PostScript -1. 0 0 1. MAarrowhead1 % End of user PostScript .5 0 1 r .5 .02381 m .02381 .5 L s % Start of user PostScript 0 -1. -1. 0 MAarrowhead1 % End of user PostScript 1 0 0 r .97619 .5 m .5 .02381 L s % Start of user PostScript 1. 0 0 -1. MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{289.563, 289.563}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHggoo00=l07ooOol0?Goo00Goo007oo00=l07ooOol0@goo00Ool5?1lTOol00g`0Oomo o`0QOol2?n0AOol00g`0Oomoo`19Ool5?n09Ool000Yoo`@l7b=oo`03O01oogoo029oo`1ll7c`OBgoo00<3ogooOol02Goo000aOol00g`0Oomoo`1LOol00g`0Oomo o`0SOol00`?oOomoo`0>Ool2?1m;Ool00`?oOomoo`0:Ool0035oo`03O01oogoo05aoo`03O01oogoo 029oo`030omoogoo00moo`03?1mooc`O04Uoo`030omoogoo00]oo`00Goo00<3ogooOol04Woo000aOol00g`0Oomoo`1LOol00g`0Oomoo`0JOol00`?oOomoo`0QOol00c`O Oomoo`0gOol00`?oOomoo`0COol0035oo`03O01oogoo05aoo`03O01oogoo01Uoo`030omoogoo02=o o`03?1moogoo03Eoo`030omoogoo01Aoo`00Ool00`?oOomoo`0iOol00c`O Oomoo`0OOol00`?oOomoo`0OOol0035oo`03O01oogoo05aoo`03O01oogoo00eoo`030omoogoo03]o o`03?1moogoo01eoo`030omoogoo021oo`00goo00=l07ooOol0O7oo00=l07ooOol07Woo00 Ool000ioo`03O01oogoo021oo`030omoogoo03Uoo`03O01oogoo07ioo`03O01oogoo021oo`03?n1o ogoo00eoo`003Goo00=l07ooOol08Goo00<3ogooOol0>7oo00=l07ooOol0Ogoo00=l07ooOol08Goo 00n0oh7oo05Qoo`Ool00coPOomoo`1LOol00`?oOomoo`0iOol0 0`?oOomoo`0>Ool00g`0Oomoo`0`Ool0035oo`030omoogoo00eoo`03?n1oogoo05aoo`030omoogoo 03]oo`030omoogoo00eoo`03O01oogoo031oo`007oo00=l07oo Ool0EGoo00<3ogooOol017oo00=l07ooOol0CGoo00goo00=l07ooOol0DWoo00<3ogooOol01goo00=l07ooOol0Agoo00Ool00`?oOomoo`0;Ool00g`0Oomo o`0oOol00c`OOomoo`0IOol00g`0Oomoo`0ROol0041oo`03O01oogoo04eoo`030omoogoo00aoo`03 O01oogoo03eoo`03?1moogoo01]oo`03O01oogoo025oo`00@Goo00=l07ooOol0C7oo00<3ogooOol0 3Goo00=l07ooOol0>goo00Ool00g`0Oomoo`0iOol00c`OOomoo`0OOol00g`0Oomoo`0OOol004=oo`03O01oogoo04Yo o`030omoogoo00moo`03O01oogoo03Moo`03?1moogoo025oo`03O01oogoo01ioo`00A7oo00=l07oo Ool0BGoo00<3ogooOol047oo00=l07ooOol0=Goo00Ool00g`0Oomoo`0oOol00`?o Oomoo`0JOol00g`0Oomoo`0QOol00c`OOomoo`0gOol00g`0Oomoo`0COol004moo`03O01oogoo03io o`030omoogoo01]oo`03O01oogoo01moo`03?1moogoo03Uoo`03O01oogoo019oo`00D7oo00=l07oo Ool0?Goo00<3ogooOol077oo00=l07ooOol07Goo00goo00=l07ooOol04Goo001AOol0 0g`0Oomoo`0lOol00`?oOomoo`0MOol00g`0Oomoo`0KOol00c`OOomoo`0mOol00g`0Oomoo`0@Ool0 059oo`03O01oogoo03]oo`030omoogoo01ioo`03O01oogoo01Uoo`03?1moogoo03moo`03O01oogoo 00moo`00Dgoo00=l07ooOol0>Woo00<3ogooOol07goo00=l07ooOol05goo001ll7c`OBWoo00=l07ooOol02Woo001FOol2?n000g`0?n0oh00eOol00`?oOomoo`0Q Ool2?n000gooO01oo`0=Ool5?1m:Ool00g`0Oomoo`09Ool005Moo`8oh003O00oh7oo03Aoo`030omo ogoo025oo`05?n0kh3oP?n1l0007oo00<3ogooOol0@goo00Ool0011oo`03?1moogoo 05aoo`03?1moogoo01ioo`030omoogoo03Yoo`030omoogoo03moo`03?n1oogoo00moo`004Goo00goo00<3ogooOol0?Goo00Ool00`?oOomoo`0GOol00coPOomoo`0SOol002Eoo`03?1moogoo05aoo`03?1moogoo00Uo o`030omoogoo04moo`030omoogoo01Eoo`03?n1oogoo02Aoo`009Woo00"], ImageRangeCache->{{{0, 288.563}, {288.563, 0}} -> {-0.0750158, -0.0750158, 0.0109163, 0.0109163}, {{6.8125, 92.75}, {281.688, 195.75}} -> {-1.21649, -1.21801, 0.0244366, 0.0244366}, {{101.313, 187.188}, {281.688, 195.75}} -> {-3.52755, -1.2189, 0.0244544, 0.0244544}, {{195.75, 281.688}, {281.688, 195.75}} -> {-5.83348, -1.21801, 0.0244366, 0.0244366}, {{6.8125, 92.75}, {187.188, 101.313}} -> {-1.21737, -3.52908, 0.0244544, 0.0244544}, {{101.313, 187.188}, {187.188, 101.313}} -> {-3.52755, -3.52908, 0.0244544, 0.0244544}, {{195.75, 281.688}, {187.188, 101.313}} -> {-5.83773, -3.52908, 0.0244544, 0.0244544}, {{6.8125, 92.75}, {92.75, 6.8125}} -> {-1.21649, -5.83501, 0.0244366, 0.0244366}, {{101.313, 187.188}, {92.75, 6.8125}} -> {-3.52755, -5.83926, 0.0244544, 0.0244544}, {{ 195.75, 281.688}, {92.75, 6.8125}} -> {-5.83348, -5.83501, 0.0244366, 0.0244366}}] }, Open ]], Cell[TextData[{ "An improvement (arguably) is to redefine ", StyleBox["DerangementGraphic", "Input"], " so that it places a border around the colored arrows, and to redefine ", StyleBox["ShowDerangementGraphics", "Input"], " to transpose the graphics array, making it wide, rather than tall." }], "Text"], Cell[BoxData[ \(DerangementGraphic[L_List] := Module[{len = Length[L], thisPoly = Poly[Length[L]], endpoints}, endpoints = Transpose[{L, Range[len]}]; Graphics[{GrayLevel[0.5], Line[1.25 Poly[len]], MapIndexed[{Hue[First[#2]/len], Arrow@@Part[thisPoly, #]}&, endpoints]}]]\)], "Input"], Cell[BoxData[ \(ShowDerangementDiagrams[n_Integer /; n > 2] := Show[GraphicsArray[ Transpose[ Partition[Map[DerangementGraphic, Derangements[n]], n - 1]]]]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(ShowDerangementDiagrams[5]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .37677 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0865801 0.00897081 0.0865801 [ [ 0 0 0 0 ] [ 1 .37677 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .37677 L 0 .37677 L closepath clip newpath % Start of user PostScript /mathtops { gsave MBeginOrig moveto MEndOrig currentpoint grestore } bind def /MAtocoords { mathtops 4 2 roll mathtops 4 copy pop pop 3 -1 roll sub /arry exch def exch sub /arrx exch def arrx dup mul arry dup mul add sqrt /arrl exch def translate } bind def /MAarrowhead1 { gsave MAtocoords arrl 0. eq { 0 0 Mdot } { [ arrx arrl div arry arrl div -1 arry mul arrl div arrx arrl div 0 0 ] concat -0.05 0.025 moveto 0 0 lineto -0.05 -0.025 lineto fill -0.05 0.025 moveto 0 0 lineto -0.05 -0.025 lineto -0.05 0.025 lineto stroke } ifelse grestore } def % End of user PostScript % Start of sub-graphic p 0.0238095 0.00897081 0.103175 0.0924202 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .77329 m .8709 .52573 L s % Start of user PostScript -0.809017 0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .57988 .12517 m .57988 .92629 L s % Start of user PostScript 0.309017 -0.951057 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .10899 .27817 m .10899 .77329 L s % Start of user PostScript -0.809017 -0.587785 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .92629 m .10899 .27817 L s % Start of user PostScript 0.309017 0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .8709 .52573 m .57988 .12517 L s % Start of user PostScript 1. 0 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.111111 0.00897081 0.190476 0.0924202 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .77329 m .8709 .52573 L s % Start of user PostScript -0.809017 0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .57988 .12517 m .57988 .92629 L s % Start of user PostScript 0.309017 -0.951057 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .92629 m .10899 .77329 L s % Start of user PostScript 0.309017 0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .8709 .52573 m .10899 .27817 L s % Start of user PostScript 1. 0 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .27817 m .57988 .12517 L s % Start of user PostScript -0.809017 -0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.198413 0.00897081 0.277778 0.0924202 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .92629 m .8709 .52573 L s % Start of user PostScript 0.309017 0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .27817 m .57988 .92629 L s % Start of user PostScript -0.809017 -0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .12517 m .10899 .77329 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .10899 .77329 m .10899 .27817 L s % Start of user PostScript -0.809017 0.587785 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .8709 .52573 m .57988 .12517 L s % Start of user PostScript 1. 0 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.285714 0.00897081 0.365079 0.0924202 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .12517 m .8709 .52573 L s % Start of user PostScript 0.309017 -0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .27817 m .57988 .92629 L s % Start of user PostScript -0.809017 -0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .92629 m .10899 .77329 L s % Start of user PostScript 0.309017 0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .8709 .52573 m .10899 .27817 L s % Start of user PostScript 1. 0 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .77329 m .57988 .12517 L s % Start of user PostScript -0.809017 0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.373016 0.00897081 0.452381 0.0924202 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .92629 m .8709 .52573 L s % Start of user PostScript 0.309017 0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .27817 m .57988 .92629 L s % Start of user PostScript -0.809017 -0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .8709 .52573 m .10899 .77329 L s % Start of user PostScript 1. 0 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .12517 m .10899 .27817 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .77329 m .57988 .12517 L s % Start of user PostScript -0.809017 0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.460317 0.00897081 0.539683 0.0924202 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .27817 m .8709 .52573 L s % Start of user PostScript -0.809017 -0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .77329 m .57988 .92629 L s % Start of user PostScript -0.809017 0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .12517 m .10899 .77329 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .8709 .52573 m .10899 .27817 L s % Start of user PostScript 1. 0 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .57988 .92629 m .57988 .12517 L s % Start of user PostScript 0.309017 0.951057 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.547619 0.00897081 0.626984 0.0924202 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .77329 m .8709 .52573 L s % Start of user PostScript -0.809017 0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .27817 m .57988 .92629 L s % Start of user PostScript -0.809017 -0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .12517 m .10899 .77329 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .8709 .52573 m .10899 .27817 L s % Start of user PostScript 1. 0 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .57988 .92629 m .57988 .12517 L s % Start of user PostScript 0.309017 0.951057 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.634921 0.00897081 0.714286 0.0924202 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .77329 m .8709 .52573 L s % Start of user PostScript -0.809017 0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .57988 .12517 m .57988 .92629 L s % Start of user PostScript 0.309017 -0.951057 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .8709 .52573 m .10899 .77329 L s % Start of user PostScript 1. 0 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .92629 m .10899 .27817 L s % Start of user PostScript 0.309017 0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .27817 m .57988 .12517 L s % Start of user PostScript -0.809017 -0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.722222 0.00897081 0.801587 0.0924202 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .27817 m .8709 .52573 L s % Start of user PostScript -0.809017 -0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .57988 .12517 m .57988 .92629 L s % Start of user PostScript 0.309017 -0.951057 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .8709 .52573 m .10899 .77329 L s % Start of user PostScript 1. 0 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .10899 .77329 m .10899 .27817 L s % Start of user PostScript -0.809017 0.587785 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .57988 .92629 m .57988 .12517 L s % Start of user PostScript 0.309017 0.951057 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.809524 0.00897081 0.888889 0.0924202 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .27817 m .8709 .52573 L s % Start of user PostScript -0.809017 -0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .57988 .12517 m .57988 .92629 L s % Start of user PostScript 0.309017 -0.951057 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .8709 .52573 m .10899 .77329 L s % Start of user PostScript 1. 0 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .92629 m .10899 .27817 L s % Start of user PostScript 0.309017 0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .77329 m .57988 .12517 L s % Start of user PostScript -0.809017 0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.896825 0.00897081 0.97619 0.0924202 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .12517 m .8709 .52573 L s % Start of user PostScript 0.309017 -0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .8709 .52573 m .57988 .92629 L s % Start of user PostScript 1. 0 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .92629 m .10899 .77329 L s % Start of user PostScript 0.309017 0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .10899 .77329 m .10899 .27817 L s % Start of user PostScript -0.809017 0.587785 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .27817 m .57988 .12517 L s % Start of user PostScript -0.809017 -0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.100765 0.103175 0.184215 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .12517 m .8709 .52573 L s % Start of user PostScript 0.309017 -0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .77329 m .57988 .92629 L s % Start of user PostScript -0.809017 0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .10899 .27817 m .10899 .77329 L s % Start of user PostScript -0.809017 -0.587785 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .92629 m .10899 .27817 L s % Start of user PostScript 0.309017 0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .8709 .52573 m .57988 .12517 L s % Start of user PostScript 1. 0 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.111111 0.100765 0.190476 0.184215 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .12517 m .8709 .52573 L s % Start of user PostScript 0.309017 -0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .77329 m .57988 .92629 L s % Start of user PostScript -0.809017 0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .92629 m .10899 .77329 L s % Start of user PostScript 0.309017 0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .8709 .52573 m .10899 .27817 L s % Start of user PostScript 1. 0 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .27817 m .57988 .12517 L s % Start of user PostScript -0.809017 -0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.198413 0.100765 0.277778 0.184215 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .92629 m .8709 .52573 L s % Start of user PostScript 0.309017 0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .57988 .12517 m .57988 .92629 L s % Start of user PostScript 0.309017 -0.951057 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .10899 .27817 m .10899 .77329 L s % Start of user PostScript -0.809017 -0.587785 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .10899 .77329 m .10899 .27817 L s % Start of user PostScript -0.809017 0.587785 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .8709 .52573 m .57988 .12517 L s % Start of user PostScript 1. 0 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.285714 0.100765 0.365079 0.184215 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .92629 m .8709 .52573 L s % Start of user PostScript 0.309017 0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .77329 m .57988 .92629 L s % Start of user PostScript -0.809017 0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .8709 .52573 m .10899 .77329 L s % Start of user PostScript 1. 0 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .12517 m .10899 .27817 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .27817 m .57988 .12517 L s % Start of user PostScript -0.809017 -0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.373016 0.100765 0.452381 0.184215 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .92629 m .8709 .52573 L s % Start of user PostScript 0.309017 0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .27817 m .57988 .92629 L s % Start of user PostScript -0.809017 -0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .12517 m .10899 .77329 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .8709 .52573 m .10899 .27817 L s % Start of user PostScript 1. 0 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .77329 m .57988 .12517 L s % Start of user PostScript -0.809017 0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.460317 0.100765 0.539683 0.184215 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .92629 m .8709 .52573 L s % Start of user PostScript 0.309017 0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .8709 .52573 m .57988 .92629 L s % Start of user PostScript 1. 0 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .12517 m .10899 .77329 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .10899 .77329 m .10899 .27817 L s % Start of user PostScript -0.809017 0.587785 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .27817 m .57988 .12517 L s % Start of user PostScript -0.809017 -0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.547619 0.100765 0.626984 0.184215 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .77329 m .8709 .52573 L s % Start of user PostScript -0.809017 0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .57988 .12517 m .57988 .92629 L s % Start of user PostScript 0.309017 -0.951057 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .10899 .27817 m .10899 .77329 L s % Start of user PostScript -0.809017 -0.587785 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .8709 .52573 m .10899 .27817 L s % Start of user PostScript 1. 0 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .57988 .92629 m .57988 .12517 L s % Start of user PostScript 0.309017 0.951057 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.634921 0.100765 0.714286 0.184215 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .12517 m .8709 .52573 L s % Start of user PostScript 0.309017 -0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .77329 m .57988 .92629 L s % Start of user PostScript -0.809017 0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .8709 .52573 m .10899 .77329 L s % Start of user PostScript 1. 0 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .92629 m .10899 .27817 L s % Start of user PostScript 0.309017 0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .27817 m .57988 .12517 L s % Start of user PostScript -0.809017 -0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.722222 0.100765 0.801587 0.184215 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .12517 m .8709 .52573 L s % Start of user PostScript 0.309017 -0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .27817 m .57988 .92629 L s % Start of user PostScript -0.809017 -0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .8709 .52573 m .10899 .77329 L s % Start of user PostScript 1. 0 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .10899 .77329 m .10899 .27817 L s % Start of user PostScript -0.809017 0.587785 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .57988 .92629 m .57988 .12517 L s % Start of user PostScript 0.309017 0.951057 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.809524 0.100765 0.888889 0.184215 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .12517 m .8709 .52573 L s % Start of user PostScript 0.309017 -0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .27817 m .57988 .92629 L s % Start of user PostScript -0.809017 -0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .8709 .52573 m .10899 .77329 L s % Start of user PostScript 1. 0 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .92629 m .10899 .27817 L s % Start of user PostScript 0.309017 0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .77329 m .57988 .12517 L s % Start of user PostScript -0.809017 0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.896825 0.100765 0.97619 0.184215 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .12517 m .8709 .52573 L s % Start of user PostScript 0.309017 -0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .8709 .52573 m .57988 .92629 L s % Start of user PostScript 1. 0 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .10899 .27817 m .10899 .77329 L s % Start of user PostScript -0.809017 -0.587785 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .92629 m .10899 .27817 L s % Start of user PostScript 0.309017 0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .77329 m .57988 .12517 L s % Start of user PostScript -0.809017 0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.192559 0.103175 0.276009 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .27817 m .8709 .52573 L s % Start of user PostScript -0.809017 -0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .77329 m .57988 .92629 L s % Start of user PostScript -0.809017 0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .92629 m .10899 .77329 L s % Start of user PostScript 0.309017 0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .12517 m .10899 .27817 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .8709 .52573 m .57988 .12517 L s % Start of user PostScript 1. 0 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.111111 0.192559 0.190476 0.276009 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .77329 m .8709 .52573 L s % Start of user PostScript -0.809017 0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .27817 m .57988 .92629 L s % Start of user PostScript -0.809017 -0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .92629 m .10899 .77329 L s % Start of user PostScript 0.309017 0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .12517 m .10899 .27817 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .8709 .52573 m .57988 .12517 L s % Start of user PostScript 1. 0 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.198413 0.192559 0.277778 0.276009 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .27817 m .8709 .52573 L s % Start of user PostScript -0.809017 -0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .57988 .12517 m .57988 .92629 L s % Start of user PostScript 0.309017 -0.951057 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .92629 m .10899 .77329 L s % Start of user PostScript 0.309017 0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .10899 .77329 m .10899 .27817 L s % Start of user PostScript -0.809017 0.587785 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .8709 .52573 m .57988 .12517 L s % Start of user PostScript 1. 0 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.285714 0.192559 0.365079 0.276009 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .92629 m .8709 .52573 L s % Start of user PostScript 0.309017 0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .77329 m .57988 .92629 L s % Start of user PostScript -0.809017 0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .12517 m .10899 .77329 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .8709 .52573 m .10899 .27817 L s % Start of user PostScript 1. 0 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .27817 m .57988 .12517 L s % Start of user PostScript -0.809017 -0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.373016 0.192559 0.452381 0.276009 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .92629 m .8709 .52573 L s % Start of user PostScript 0.309017 0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .57988 .12517 m .57988 .92629 L s % Start of user PostScript 0.309017 -0.951057 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .10899 .27817 m .10899 .77329 L s % Start of user PostScript -0.809017 -0.587785 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .8709 .52573 m .10899 .27817 L s % Start of user PostScript 1. 0 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .77329 m .57988 .12517 L s % Start of user PostScript -0.809017 0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.460317 0.192559 0.539683 0.276009 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .92629 m .8709 .52573 L s % Start of user PostScript 0.309017 0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .57988 .12517 m .57988 .92629 L s % Start of user PostScript 0.309017 -0.951057 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .8709 .52573 m .10899 .77329 L s % Start of user PostScript 1. 0 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .10899 .77329 m .10899 .27817 L s % Start of user PostScript -0.809017 0.587785 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .27817 m .57988 .12517 L s % Start of user PostScript -0.809017 -0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.547619 0.192559 0.626984 0.276009 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .12517 m .8709 .52573 L s % Start of user PostScript 0.309017 -0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .77329 m .57988 .92629 L s % Start of user PostScript -0.809017 0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .10899 .27817 m .10899 .77329 L s % Start of user PostScript -0.809017 -0.587785 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .8709 .52573 m .10899 .27817 L s % Start of user PostScript 1. 0 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .57988 .92629 m .57988 .12517 L s % Start of user PostScript 0.309017 0.951057 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.634921 0.192559 0.714286 0.276009 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .77329 m .8709 .52573 L s % Start of user PostScript -0.809017 0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .8709 .52573 m .57988 .92629 L s % Start of user PostScript 1. 0 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .10899 .27817 m .10899 .77329 L s % Start of user PostScript -0.809017 -0.587785 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .12517 m .10899 .27817 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .57988 .92629 m .57988 .12517 L s % Start of user PostScript 0.309017 0.951057 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.722222 0.192559 0.801587 0.276009 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .77329 m .8709 .52573 L s % Start of user PostScript -0.809017 0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .8709 .52573 m .57988 .92629 L s % Start of user PostScript 1. 0 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .92629 m .10899 .77329 L s % Start of user PostScript 0.309017 0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .12517 m .10899 .27817 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .27817 m .57988 .12517 L s % Start of user PostScript -0.809017 -0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.809524 0.192559 0.888889 0.276009 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .12517 m .8709 .52573 L s % Start of user PostScript 0.309017 -0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .8709 .52573 m .57988 .92629 L s % Start of user PostScript 1. 0 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .10899 .27817 m .10899 .77329 L s % Start of user PostScript -0.809017 -0.587785 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .10899 .77329 m .10899 .27817 L s % Start of user PostScript -0.809017 0.587785 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .57988 .92629 m .57988 .12517 L s % Start of user PostScript 0.309017 0.951057 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.896825 0.192559 0.97619 0.276009 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .27817 m .8709 .52573 L s % Start of user PostScript -0.809017 -0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .8709 .52573 m .57988 .92629 L s % Start of user PostScript 1. 0 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .92629 m .10899 .77329 L s % Start of user PostScript 0.309017 0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .12517 m .10899 .27817 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .77329 m .57988 .12517 L s % Start of user PostScript -0.809017 0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.284354 0.103175 0.367803 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .27817 m .8709 .52573 L s % Start of user PostScript -0.809017 -0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .77329 m .57988 .92629 L s % Start of user PostScript -0.809017 0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .12517 m .10899 .77329 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .92629 m .10899 .27817 L s % Start of user PostScript 0.309017 0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .8709 .52573 m .57988 .12517 L s % Start of user PostScript 1. 0 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.111111 0.284354 0.190476 0.367803 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .77329 m .8709 .52573 L s % Start of user PostScript -0.809017 0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .27817 m .57988 .92629 L s % Start of user PostScript -0.809017 -0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .12517 m .10899 .77329 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .92629 m .10899 .27817 L s % Start of user PostScript 0.309017 0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .8709 .52573 m .57988 .12517 L s % Start of user PostScript 1. 0 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.198413 0.284354 0.277778 0.367803 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .12517 m .8709 .52573 L s % Start of user PostScript 0.309017 -0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .27817 m .57988 .92629 L s % Start of user PostScript -0.809017 -0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .92629 m .10899 .77329 L s % Start of user PostScript 0.309017 0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .10899 .77329 m .10899 .27817 L s % Start of user PostScript -0.809017 0.587785 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .8709 .52573 m .57988 .12517 L s % Start of user PostScript 1. 0 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.285714 0.284354 0.365079 0.367803 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .92629 m .8709 .52573 L s % Start of user PostScript 0.309017 0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .77329 m .57988 .92629 L s % Start of user PostScript -0.809017 0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .10899 .27817 m .10899 .77329 L s % Start of user PostScript -0.809017 -0.587785 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .12517 m .10899 .27817 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .8709 .52573 m .57988 .12517 L s % Start of user PostScript 1. 0 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.373016 0.284354 0.452381 0.367803 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .27817 m .8709 .52573 L s % Start of user PostScript -0.809017 -0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .57988 .12517 m .57988 .92629 L s % Start of user PostScript 0.309017 -0.951057 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .92629 m .10899 .77329 L s % Start of user PostScript 0.309017 0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .8709 .52573 m .10899 .27817 L s % Start of user PostScript 1. 0 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .77329 m .57988 .12517 L s % Start of user PostScript -0.809017 0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.460317 0.284354 0.539683 0.367803 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .57988 .92629 m .8709 .52573 L s % Start of user PostScript 0.309017 0.951057 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .8709 .52573 m .57988 .92629 L s % Start of user PostScript 1. 0 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .10899 .27817 m .10899 .77329 L s % Start of user PostScript -0.809017 -0.587785 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .12517 m .10899 .27817 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .77329 m .57988 .12517 L s % Start of user PostScript -0.809017 0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.547619 0.284354 0.626984 0.367803 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .27817 m .8709 .52573 L s % Start of user PostScript -0.809017 -0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .77329 m .57988 .92629 L s % Start of user PostScript -0.809017 0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .8709 .52573 m .10899 .77329 L s % Start of user PostScript 1. 0 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .12517 m .10899 .27817 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .57988 .92629 m .57988 .12517 L s % Start of user PostScript 0.309017 0.951057 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.634921 0.284354 0.714286 0.367803 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .77329 m .8709 .52573 L s % Start of user PostScript -0.809017 0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .10899 .27817 m .57988 .92629 L s % Start of user PostScript -0.809017 -0.587785 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .8709 .52573 m .10899 .77329 L s % Start of user PostScript 1. 0 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .12517 m .10899 .27817 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .57988 .92629 m .57988 .12517 L s % Start of user PostScript 0.309017 0.951057 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.722222 0.284354 0.801587 0.367803 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .77329 m .8709 .52573 L s % Start of user PostScript -0.809017 0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .8709 .52573 m .57988 .92629 L s % Start of user PostScript 1. 0 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .12517 m .10899 .77329 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .92629 m .10899 .27817 L s % Start of user PostScript 0.309017 0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .27817 m .57988 .12517 L s % Start of user PostScript -0.809017 -0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.809524 0.284354 0.888889 0.367803 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .27817 m .8709 .52573 L s % Start of user PostScript -0.809017 -0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .8709 .52573 m .57988 .92629 L s % Start of user PostScript 1. 0 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .12517 m .10899 .77329 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .10899 .77329 m .10899 .27817 L s % Start of user PostScript -0.809017 0.587785 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .57988 .92629 m .57988 .12517 L s % Start of user PostScript 0.309017 0.951057 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.896825 0.284354 0.97619 0.367803 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.421171 0.525731 0.421171 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s .8 1 0 r .10899 .27817 m .8709 .52573 L s % Start of user PostScript -0.809017 -0.587785 1. 0 MAarrowhead1 % End of user PostScript 0 1 .4 r .8709 .52573 m .57988 .92629 L s % Start of user PostScript 1. 0 0.309017 0.951057 MAarrowhead1 % End of user PostScript 0 .4 1 r .57988 .12517 m .10899 .77329 L s % Start of user PostScript 0.309017 -0.951057 -0.809017 0.587785 MAarrowhead1 % End of user PostScript .8 0 1 r .57988 .92629 m .10899 .27817 L s % Start of user PostScript 0.309017 0.951057 -0.809017 -0.587785 MAarrowhead1 % End of user PostScript 1 0 0 r .10899 .77329 m .57988 .12517 L s % Start of user PostScript -0.809017 0.587785 0.309017 -0.951057 MAarrowhead1 % End of user PostScript MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{593, 223.063}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol0106OO01l07`00Woo00 Ool2?NlEOol0106OOomoog`01goo00Ool00cg_Oomoo`03Ool00f@OOomo o`03I1l:Ool00g`0Oomoo`09Ool00cg_Oomoo`0>Ool00cg_Oomoo`0COol01@6OOomoogooO00027oo 00Ool00g`0Oomoo`06Ool00fOPOomoo`02Ool00cg_Oomoo`0=Ool00cg_Oomoo`02Ool4I1l=Ool0 0g`0Oomoo`0:Ool00cg_Oomoo`0=Ool00cg_Oomoo`03Ool2I1l>Ool01@6OOomoogooO0002Goo00 Ool00`6OOomoo`02Ool00g`0Oomoo`07Ool00cg_Oomoo`0Ool00g`0Oomo o`08Ool00cg_Oomoo`0;Ool013g_Oomoogoo0V@O0goo16OP1Woo00=l07ooOol017oo00<3k7ooOol0 2Goo00Ool00fOPOomoo`02Ool00cg_Oomoo`09Ool00cg_Oomoo`04Ool00`?/Oomoo`08Ool00g`0Oomo o`0BOol00cg_Oomoo`09Ool00cg_Oomoo`0=Ool3I1l7Ool00g`0Oomoo`0;Ool00cg_Oomoo`09Ool0 0cg_Oomoo`04Ool00`?/Oomoo`06Ool3I1l7Ool00g`0Oomoo`0:Ool00cg_Oomoo`09Ool00cg_Oomo o`04Ool00f@OOomoo`0@Ool00`?/Oomoo`0;Ool00cg_Oomoo`09Ool01Cg_OomoogooI1l02goo0fOP 1goo00=l07ooOol02Woo00Ool00`6OOomT7`02I1l4Ool00g`0Oomoo`0Ool00`?/Oomoo`08Ool01G`0Oomoogoo?Nl02Goo00Ool00cg_Oomoo`06Ool01Cg_OomoogooI1l05Goo00=l07oo In000fOP2Woo00Ool30Il5Ool3In02Ool00cg_Oomoo`06Ool00cg_Oomoo`08Ool00`6OOomoo`0Ool00cg_Oomoo`06Ool00cg_Oomoo`08Ool0106OOomoo`?/2goo00=l07ooOol00fOP 2Woo00Ool00`?/Oomoo`09Ool00cg_Oomoo`0;Ool01Sg_OomoogooI1l1 W`eoo`030naoogoo00Yoo`03In1oogoo009oo`03?Nmoogoo00]oo`03?Nmoogoo009oo`03O01oogoo 00]oo`030naoogoo011oo`03?Nmoogoo00]oo`03?Nmoogoo009oo`04O001WgooOol30Il7Ool00`?/ Oomoo`0:Ool00fOPOomoo`02Ool00cg_Oomoo`0;Ool00cg_Oomoo`02Ool20IlCOol00g`0Oomoo`09 Ool00cg_Oomoo`0;Ool013g_Oomoogoo0P6O0goo0fOP1goo00<3k7ooOol017oo00=l07ooOol027oo 00Ool00g`0Oomoo`08Ool00cg_Oomoo`0; Ool00cg_Oomoo`02Ool017`00Imoogoo0`6O1goo00=T7gooOol017oo00<3k7ooOol02Goo00Ool00cg_Oomoo`03Ool00`6OOomoo`030Il>Ool00`?/Oomoo`06Ool00cg_Oomo o`0>Ool00cg_Oomoo`0COol00`?/Oomoo`04Ool00fOPOomoo`02Ool00cg_Oomoo`0>Ool00cg_Oomo o`03Ool00`6OOomoo`030Il:Ool00`?/Oomoo`0:Ool00cg_Oomoo`0>Ool00cg_Oomoo`0COol00`?/ Oomoo`04Ool00fOPOomoo`02Ool00cg_Oomoo`0>Ool00cg_Oomoo`06Ool30n`>Ool00g`0Oomoo`06 Ool00cg_Oomoo`0>Ool00cg_Oomoo`0COol01@?/OomoogooO0001goo00Ool2?Nl:Ool4O00COol00cg_Oomoo`0> Ool2?NlEOol00g`0Oomoo`08Ool00cg_Oomoo`0>Ool2?Nl:Ool4O007Ool00`6OOomoo`09Ool00cg_ Oomoo`0>Ool2?NlHOol00g`0Oomoo`05Ool00cg_Oomoo`0>Ool2?Nl:Ool4O00=Ool00fOPOomoo`03 Ool00cg_Oomoo`0>Ool2?NlHOol017`0OomoofOP17oo00Ool0 0cg_Oomoo`0COol00g`0Oomoo`05Ool00fOPOomoo`02Ool00cg_Oomoo`0=Ool00cg_Oomoo`0COol0 0g`0Oomoo`05Ool00fOPOomoo`02Ool00cg_Oomoo`0IOol0011oo`03?Nmoogoo01aoo`05O01oogoo Oolmk`0?Ool00cg_Oomoo`03Ool3O00FOol00fOPOomoo`02Ool00cg_Oomoo`0=Ool00cg_Oomoo`0G Ool01@?/OomoogooO00017oo00Ool00cg_Oomoo`0;Ool01Sg_Oomoof@OH1mT7`ioo`030Imoogoo00mo o`03?Nmoogoo00]oo`05?NmoogooOol1W`04I1lAOol00g`0Oomoo`08Ool00cg_Oomoo`0;Ool013g_ Oomoogoo0f@O6Goo00=Wh7ooOol00goo00Ool00g`0Oomoo`08Ool00cg_ Oomoo`0;Ool013g_Oomoogoo0V@O6goo00=Wh7ooOol00Woo00Ool00fOPOomoo`02Ool00cg_Oomoo`08Ool01Cg_Oomoogoo0Il00Woo 00=T7gooOol027oo00=l07ooOol03Woo00=Wh7ooOol00Woo00Ool00cg_Oomoo`07Ool01Cg_Oomoogoo0Il017oo00=l 07ooOol017oo00=T7gooOol04Goo00<3k7ooOol00Woo00Ool016@O0Il1W`6O4goo00Ool00f@OOomoo`0@Ool00cg_Oomoo`0:Ool00cg_Oomoo`0TOol0 0cg_Oomoo`0:Ool01Cg_OomoogooI1l05Goo00<3k7ooOol017oo00=Wh7ooOol00Woo00Ool00g`0Oomoo`08Ool00cg_Oomoo`0;Ool00cg_Oomo o`03Ool00`6OOomoo`030Il7Ool00f@OOomoo`0@Ool00cg_Oomoo`0;Ool01Sg_OomoogooI1l1W`=o o`<1W`Moo`030naoogoo00Aoo`03O01oogoo00Qoo`03?Nmoogoo00]oo`03?Nmoogoo009oo`04O001 WgooOol30Il7Ool00f@OOomoo`0@Ool00cg_Oomoo`0:Ool00cg_Oomoo`020Il00g`00Imoo`0;Ool0 0f@OOomoo`0;Ool00`?/Oomoo`02Ool00cg_Oomoo`0FOol0011oo`05?NmoogooOol1W`0?Ool00f@O Oomoo`0=Ool00cg_Oomoo`0Ool00f@OOomoo`09Ool00`?/Oomoo`02Ool00cg_Oomo o`0GOol0011oo`06?NmoogooOol1W`?/3goo00=T7gooOol02goo00Ool00cg_Oomoo`0COol00f@OOomoo`0:Ool00cg_ Oomoo`0=Ool00cg_Oomoo`0COol00f@OOomoo`05Ool00`?/Oomoo`02Ool00cg_Oomoo`0IOol0011o o`8mk`Yoo`<3k0Qoo`03I1moogoo00Moo`03?Nmoogoo00moo`8mk`Yoo`<1Wa=oo`03?Nmoogoo00mo o`8mkaQoo`040naoogooIn03Ool00cg_Oomoo`0?Ool2?Nl:Ool30n`>Ool00fOPOomoo`02Ool00cg_ Oomoo`0?Ool2?NlEOol00`?/Oomoo`03Ool01FOPOomoogoo?Nl04Goo0Sg_6goo00<3k7ooOol00Woo 00Ool00cg_Oomoo`0AOol3?NlEOol00g`0OomWh005Ool00cg_Oomoo`0@Ool3?Nl;Ool3 I1l5Ool00g`0Oomoo`07Ool00cg_Oomoo`0JOol0011oo`8mk`Yoo`AT7`eoo`05O01oogooOolmk`0A Ool2?Nl:Ool4I1l=Ool00g`0Oomoo`02Ool00cg_Oomoo`0?Ool2?NlHOol010?/Oomoog`00goo00Ool00cg_Oomoo`06Ool3O00>Ool00`?/Oomoo`06Ool00cg_Oomoo`0>Ool00cg_Oomoo`0G Ool017`0OomoofOP17oo00Ool00g`0Oomo o`03Ool00fOPOomoo`02Ool00cg_Oomoo`0;Ool01Cg_Oomoogoo0Il05Goo00=l07ooOol02Goo00Ool0106OI1mT7f@O4goo00Ool00cg_Oomo o`06Ool00cg_Oomoo`0WOol00cg_Oomoo`06Ool01Cg_OomoogooI1l05Goo00=l07ooOol02Goo0VOP 0goo00Ool00cg_Oomoo`05Ool00cg_Oomoo`08Ool00`6OOomoo`0HOol2In04Ool0 0cg_Oomoo`05Ool01Cg_Oomoogoo0Il01Woo00=l07ooOol037oo00<3k7ooOol027oo0fOP0goo00Ool00cg_Oomoo`05Ool01Cg_Oomoogoo0Il05Goo 00=l07ooOol01goo0fOP00<3k7ooOol00Woo00Ool00`?/OomWh003In0BOol00cg_Oomoo`08 Ool01Cg_OomoogooI1l05Goo00<3k7ooOol02goo00Ool40Il3Ool00`?/ Oomoo`06Ool00fOPOomoo`03Ool00cg_Oomoo`08Ool01Cg_Oomoogoo0Il05Goo00=l07ooOol02goo 00Ool00cg_Oomoo`03Ool00`6OOomoo`030Il:Ool0 0`?/Oomoo`0:Ool00cg_Oomoo`0>Ool00cg_Oomoo`03Ool00`6OOomoo`030Il>Ool00`?/Oomoo`05 Ool00cg_Oomoo`0>Ool00cg_Oomoo`06Ool30n`BOol00fOPOomoo`02Ool00cg_Oomoo`0>Ool00cg_ Oomoo`0GOol01@?/OomoogooIn000goo00Ool00cg_Oomoo`02Ool0106OOomoogoo 0`6O4Woo00D3k7ooOomoocg_011oo`03?Nmoogoo01Moo`05O01oogooOol3k004Ool00cg_Oomoo`0= Ool00cg_Oomoo`03Ool00`6OOomoo`030IlBOol00`?/Oomoo`02Ool00cg_Oomoo`0IOol0011oo`8m k`Yoo`<1Wa=oo`03?Nmoogoo00ioo`8mk`Yoo`<1W`Qoo`030naoogoo00Uoo`03?Nmoogoo00ioo`8m k`Yoo`<1W`]oo`030naoogoo00Eoo`03?Nmoogoo00ioo`8mk`Yoo`<3k0ioo`03In1oogoo00=oo`03 ?Nmoogoo00ioo`8mkaQoo`040naoogooIn04Ool00cg_Oomoo`0>Ool2?NlHOol010?/OomoofOP1Goo 00Ool00`?/Oomoo`03Ool00cg_Oomoo`0I Ool0019oo`Ool0 0`6OO01l0002O002Ool00cg_Oomoo`0IOol3?Nl?Ool3O002Ool00cg_Oomoo`0IOol3?Nl;Ool3I1l0 0gooO01l0002O002Ool00cg_Oomoo`0IOol3?NlOol3O004Ool00cg_Oomoo`0HOol3 ?Nl=Ool3O005Ool00cg_Oomoo`0LOol001Eoo`Ool2?NlEOol00g`0Oomoo`08 Ool00cg_Oomoo`0JOol0011oo`03?Nmoogoo01=oo`030Imoogoo00Eoo`05O01oogooOolmk`0@Ool0 0cg_Oomoo`0COol00`6OOomoo`05Ool00g`0Oomoo`02Ool00cg_Oomoo`0>Ool00cg_Oomoo`0JOol0 0g`0Oomoo`02Ool00cg_Oomoo`0>Ool00cg_Oomoo`03Ool00f@OOomoo`03I1lBOol00g`0Oomoo`02 Ool00cg_Oomoo`0>Ool00cg_Oomoo`0COol01G`0Oomoogoo0n`01goo00Ool0 1G`0Oomoogoo?Nl02goo00Ool0 17`0I1mT7f@O1Goo00<3k7ooOol02Woo00Ool00cg_Oomoo`06Ool00cg_Oomoo`08Ool016@O Oomoo`6O6goo00Ool00cg_Oomoo`05Ool01Cg_Oomoogoo 0Il01Woo00=l07ooOol067oo00<3k6OPOol00goo00Ool00`?/Ool1W`030Il3Ool00g`0Oomoo`0Ool00g`0Oomoo`08Ool00cg_Oomoo`0;Ool00cg_Oomo o`03Ool00`6OOomoo`040Il6Ool00`?/Oomoo`04Ool00g`0Oomoo`09Ool00cg_Oomoo`0;Ool013g_ Oomoogoo0P6O0goo0fOP1goo00=T7gooOol02Woo00<3k7ooOol00Woo00Ool00cg_Oomoo`0;Ool013g_Oomoogoo106O00=Wh7ooOol02Goo00=T 7gooOol03goo00Ool00`?/Oomoo`0Ool2?NlEOol00f@OOomoo`09Ool00cg_Oomoo`0>Ool2?Nl: Ool30Il8Ool00`?/Oomoo`08Ool00cg_Oomoo`0>Ool2?Nl:Ool30n`>Ool00fOPOomoo`03Ool00cg_ Oomoo`0>Ool2?Nl:Ool30Il;Ool00`?/Oomoo`05Ool00cg_Oomoo`0>Ool2?NlKOol00`?/Oomoo`03 Ool00cg_Oomoo`0>Ool2?Nl:Ool30n`;Ool00g`0Oomoo`05Ool00cg_Oomoo`0>Ool2?NlEOol010?/ Oomoog`027oo00Ool00f@O0n`3j`020n`2Ool0 0cg_Oomoo`0LOol001]oo`"], ImageRangeCache->{{{0, 592}, {222.063, 0}} -> {-0.300683, -0.103635, 0.0195969, 0.0195969}, {{15.3125, 62.0625}, {216.75, 167.563}} -> {-1.84551, -1.51889, 0.0507884, 0.0507884}, {{66.75, 113.563}, {216.75, 167.563}} -> {-4.45657, -1.51791, 0.0507556, 0.0507556}, {{118.25, 165}, {216.75, 167.563}} -> {-7.07354, -1.51889, 0.0507884, 0.0507884}, {{169.688, 216.438}, {216.75, 167.563}} -> {-9.68596, -1.51889, 0.0507884, 0.0507884}, {{221.125, 267.875}, {216.75, 167.563}} -> {-12.2984, -1.51889, 0.0507884, 0.0507884}, {{272.563, 319.375}, {216.75, 167.563}} -> {-14.9027, -1.51791, 0.0507556, 0.0507556}, {{324.063, 370.813}, {216.75, 167.563}} -> {-17.5264, -1.51889, 0.0507884, 0.0507884}, {{375.5, 422.25}, { 216.75, 167.563}} -> {-20.1388, -1.51889, 0.0507884, 0.0507884}, {{426.938, 473.75}, {216.75, 167.563}} -> {-22.7381, -1.51791, 0.0507556, 0.0507556}, {{478.375, 525.188}, {216.75, 167.563}} -> {-25.3488, -1.51791, 0.0507556, 0.0507556}, {{529.875, 576.625}, {216.75, 167.563}} -> {-27.9793, -1.51889, 0.0507884, 0.0507884}, {{15.3125, 62.0625}, {162.625, 113.438}} -> {-1.84551, -4.26781, 0.0507884, 0.0507884}, {{66.75, 113.563}, {162.625, 113.438}} -> {-4.45657, -4.26506, 0.0507556, 0.0507556}, {{118.25, 165}, {162.625, 113.438}} -> {-7.07354, -4.26781, 0.0507884, 0.0507884}, {{169.688, 216.438}, {162.625, 113.438}} -> {-9.68596, -4.26781, 0.0507884, 0.0507884}, {{221.125, 267.875}, {162.625, 113.438}} -> {-12.2984, -4.26781, 0.0507884, 0.0507884}, {{272.563, 319.375}, {162.625, 113.438}} -> {-14.9027, -4.26506, 0.0507556, 0.0507556}, {{324.063, 370.813}, {162.625, 113.438}} -> {-17.5264, -4.26781, 0.0507884, 0.0507884}, {{375.5, 422.25}, { 162.625, 113.438}} -> {-20.1388, -4.26781, 0.0507884, 0.0507884}, {{ 426.938, 473.75}, {162.625, 113.438}} -> {-22.7381, -4.26506, 0.0507556, 0.0507556}, {{478.375, 525.188}, {162.625, 113.438}} -> {-25.3488, -4.26506, 0.0507556, 0.0507556}, {{529.875, 576.625}, {162.625, 113.438}} -> {-27.9793, -4.26781, 0.0507884, 0.0507884}, {{15.3125, 62.0625}, {108.563, 59.375}} -> {-1.84551, -7.01356, 0.0507884, 0.0507884}, {{66.75, 113.563}, {108.563, 59.375}} -> {-4.45657, -7.00903, 0.0507556, 0.0507556}, {{118.25, 165}, { 108.563, 59.375}} -> {-7.07354, -7.01356, 0.0507884, 0.0507884}, {{169.688, 216.438}, {108.563, 59.375}} -> {-9.68596, -7.01356, 0.0507884, 0.0507884}, {{221.125, 267.875}, {108.563, 59.375}} -> {-12.2984, -7.01356, 0.0507884, 0.0507884}, {{272.563, 319.375}, {108.563, 59.375}} -> {-14.9027, -7.00903, 0.0507556, 0.0507556}, {{324.063, 370.813}, {108.563, 59.375}} -> {-17.5264, -7.01356, 0.0507884, 0.0507884}, {{375.5, 422.25}, {108.563, 59.375}} -> {-20.1388, -7.01356, 0.0507884, 0.0507884}, {{426.938, 473.75}, {108.563, 59.375}} -> {-22.7381, -7.00903, 0.0507556, 0.0507556}, {{478.375, 525.188}, {108.563, 59.375}} -> {-25.3488, -7.00903, 0.0507556, 0.0507556}, {{529.875, 576.625}, {108.563, 59.375}} -> {-27.9793, -7.01356, 0.0507884, 0.0507884}, {{15.3125, 62.0625}, {54.4375, 5.25}} -> {-1.84551, -9.76248, 0.0507884, 0.0507884}, {{66.75, 113.563}, { 54.4375, 5.25}} -> {-4.45657, -9.75618, 0.0507556, 0.0507556}, {{118.25, 165}, {54.4375, 5.25}} -> {-7.07354, -9.76248, 0.0507884, 0.0507884}, {{ 169.688, 216.438}, {54.4375, 5.25}} -> {-9.68596, -9.76248, 0.0507884, 0.0507884}, {{221.125, 267.875}, {54.4375, 5.25}} -> {-12.2984, -9.76248, 0.0507884, 0.0507884}, {{272.563, 319.375}, {54.4375, 5.25}} -> {-14.9027, -9.75618, 0.0507556, 0.0507556}, {{324.063, 370.813}, { 54.4375, 5.25}} -> {-17.5264, -9.76248, 0.0507884, 0.0507884}, {{375.5, 422.25}, {54.4375, 5.25}} -> {-20.1388, -9.76248, 0.0507884, 0.0507884}, {{ 426.938, 473.75}, {54.4375, 5.25}} -> {-22.7381, -9.75618, 0.0507556, 0.0507556}, {{478.375, 525.188}, {54.4375, 5.25}} -> {-25.3488, -9.75618, 0.0507556, 0.0507556}, {{529.875, 576.625}, {54.4375, 5.25}} -> {-27.9793, -9.76248, 0.0507884, 0.0507884}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Bell numbers", "Section"], Cell[TextData[{ "The Bell numbers (denoted ", Cell[BoxData[ \(TraditionalForm\`B\_n\)]], ") are the numbers of ways to partition a set into disjoint, non-empty \ subsets. For example, the set ", Cell[BoxData[ \(TraditionalForm\`{1, 2}\)]], " can be partitioned in the following two ways." }], "Text"], Cell[TextData[Cell[BoxData[ InterpretationBox[GridBox[{ {\({{1}, {2}}\)}, {\({{1, 2}}\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ {{{1}, {2}}, {{1, 2}}}], Editable->False]]]], "Text"], Cell[TextData[{ "Similarly, the set ", Cell[BoxData[ \(TraditionalForm\`{1, 2, 3}\)]], " can be partitioned in the following five ways." }], "Text"], Cell[TextData[Cell[BoxData[ InterpretationBox[GridBox[{ {\({{1}, {2}, {3}}\)}, {\({{1, 2}, {3}}\)}, {\({{1, 3}, {2}}\)}, {\({{1}, {2, 3}}\)}, {\({{1, 2, 3}}\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ {{{1}, {2}, {3}}, {{1, 2}, {3}}, {{1, 3}, {2}}, {{1}, {2, 3}}, {{1, 2, 3}}}], Editable->False]], "Input", FontWeight->"Plain"]], "Text"], Cell[TextData[{ "We can recursively compute the lists of Bell partitions by noting that the \ partitions of a set with ", Cell[BoxData[ \(TraditionalForm\`n\)]], " elements can be created by appending the ", StyleBox["singleton", FontSlant->"Italic"], " ", Cell[BoxData[ \(TraditionalForm\`{n}\)]], " to each list of partitions of ", Cell[BoxData[ \(TraditionalForm\`n - 1\)]], " elements, or by appending the ", StyleBox["element", FontSlant->"Italic"], " ", Cell[BoxData[ \(TraditionalForm\`n\)]], " to each partition of ", Cell[BoxData[ \(TraditionalForm\`n - 1\)]], " elements. An example: starting with the two partitions of ", Cell[BoxData[ \(TraditionalForm\`{1, 2}\)]], ", we can create the partitions ", Cell[BoxData[ \(TraditionalForm\`{{1}, {2}, {3}}\)]], " and ", Cell[BoxData[ \(TraditionalForm\`{{1, 2}, {3}}\)]], " using the first case, and the partitions ", Cell[BoxData[ \(TraditionalForm\`{{1, 3}, {2}}, \ {{1}, {2, 3}}\)]], ", and ", Cell[BoxData[ \(TraditionalForm\`{{1, 2, 3}}\)]], " using the second case." }], "Text"], Cell[TextData[{ "First we translate our two cases into ", StyleBox["Mathematica", FontSlant->"Italic"], " rules." }], "Text"], Cell[BoxData[ \(BellRule1[n_] = {S__} \[Rule] {S, {n}}; \n BellRule2[n_] = {b___, {S__}, a___} \[Rule] {b, {S, n}, a}; \)], "Input"], Cell[TextData[{ "Here we generate the list of partitions making up ", Cell[BoxData[ \(TraditionalForm\`B\_3\)]], " given the list of partitions making up ", Cell[BoxData[ \(TraditionalForm\`B\_2\)]], "." }], "Text"], Cell[BoxData[ \(\(B2 = {{{1}, {2}}, {{1, 2}}}; \)\)], "Input"], Cell["These are the partitions generated from the first rule.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Map[ReplaceList[#, BellRule1[3]]&, B2]\)], "Input"], Cell[BoxData[ \({{{{1}, {2}, {3}}}, {{{1, 2}, {3}}}}\)], "Output"] }, Open ]], Cell["And these are the partitions generated from the second rule.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(Map[ReplaceList[#, BellRule2[3]]&, B2]\)], "Input"], Cell[BoxData[ \({{{{1, 3}, {2}}, {{1}, {2, 3}}}, {{{1, 2, 3}}}}\)], "Output"] }, Open ]], Cell["\<\ The following definitions generate the complete list of Bell \ partitions.\ \>", "Text"], Cell[BoxData[ \(\(BellLists[1] = {{{1}}}; \)\)], "Input"], Cell[BoxData[ \(BellLists[n_Integer?Positive] := \(BellLists[n] = \n\t\t Flatten[\n\t\t\t\t Map[ReplaceList[#, {BellRule1[n], BellRule2[n]}]&, BellLists[n - 1]], 1]\)\)], "Input"], Cell[TextData[{ "Here is the complete list of partitions making up ", Cell[BoxData[ \(TraditionalForm\`B\_3\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(BellLists[3] // ColumnForm\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {\({{1}, {2}, {3}}\)}, {\({{1, 3}, {2}}\)}, {\({{1}, {2, 3}}\)}, {\({{1, 2}, {3}}\)}, {\({{1, 2, 3}}\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ {{{1}, {2}, {3}}, {{1, 3}, {2}}, {{1}, {2, 3}}, {{1, 2}, { 3}}, {{1, 2, 3}}}], Editable->False]], "Output"] }, Open ]], Cell[TextData[{ "And here is the complete list making up ", Cell[BoxData[ \(TraditionalForm\`B\_4\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(BellLists[4] // ColumnForm\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {\({{1}, {2}, {3}, {4}}\)}, {\({{1, 2}, {3}, {4}}\)}, {\({{1, 3}, {2}, {4}}\)}, {\({{1}, {2, 3}, {4}}\)}, {\({{1, 2, 3}, {4}}\)}, {\({{1, 4}, {2}, {3}}\)}, {\({{1}, {2, 4}, {3}}\)}, {\({{1}, {2}, {3, 4}}\)}, {\({{1, 2, 4}, {3}}\)}, {\({{1, 2}, {3, 4}}\)}, {\({{1, 3, 4}, {2}}\)}, {\({{1, 3}, {2, 4}}\)}, {\({{1, 4}, {2, 3}}\)}, {\({{1}, {2, 3, 4}}\)}, {\({{1, 2, 3, 4}}\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ {{{1}, {2}, {3}, {4}}, {{1, 2}, {3}, {4}}, {{1, 3}, {2}, { 4}}, {{1}, {2, 3}, {4}}, {{1, 2, 3}, {4}}, {{1, 4}, {2}, {3}}, {{1}, { 2, 4}, {3}}, {{1}, {2}, {3, 4}}, {{1, 2, 4}, {3}}, {{1, 2}, {3, 4}}, {{1, 3, 4}, {2}}, {{1, 3}, {2, 4}}, {{1, 4}, {2, 3}}, {{1}, {2, 3, 4}}, {{1, 2, 3, 4}}}], Editable->False]], "Output"] }, Open ]], Cell[TextData[{ "To visualize the partitions contributing to the ", Cell[BoxData[ \(TraditionalForm\`n\^th\)]], " Bell number, we arrange ", StyleBox["n", FontSlant->"Italic"], " points (representing the ", StyleBox["n", FontSlant->"Italic"], " elements) along the circumference of a circle, and then connect points in \ the same subset with a line loop. (For a singleton ", Cell[BoxData[ \(TraditionalForm\`{k}\)]], " in a Bell list, we display a point.) Because the diagrams represent \ unordered lists, it is not necessary to use colors or arrows to distinguish \ different Bell lists." }], "Text"], Cell[BoxData[ \(Loop[ptL_List] := Line[Append[ptL, First[ptL]]]\)], "Input"], Cell[BoxData[ \(BellDiagram[L_List] := Module[{thisPoly = Poly[Max[L]], frm}, frm = {GrayLevel[0.5], Line[1.5 thisPoly]}; Graphics[{frm, Map[Loop, Map[thisPoly\[LeftDoubleBracket]#\[RightDoubleBracket]&, L]]}]] \)], "Input"], Cell[TextData[{ "Here is the diagram corresponding to the Bell list ", Cell[BoxData[ \(TraditionalForm\`{{1, 2}, {3}}\)]], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[BellDiagram[{{1, 2}, {3}}]]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1.1547 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.34127 0.42328 0.57735 0.42328 [ [ 0 0 0 0 ] [ 1 1.1547 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.1547 L 0 1.1547 L closepath clip newpath .5 g .5 Mabswid .97619 .57735 m .02381 1.12721 L .02381 .02749 L .97619 .57735 L s 0 g .76455 .57735 m .12963 .94392 L .76455 .57735 L s .12963 .21078 m .12963 .21078 L s % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{84.375, 97.4375}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg7oo0P0047oo0Sg_1Goo00000goo?Nmoo`0g Ool00`00Oomoo`0>Ool2?Nl7Ool00003Oolmkgoo03Eoo`80011oo`03?Nmoogoo00Moo`0000=oocg_ Ool0 Ool2?NlVOol00003Oolmkgoo01Ioo`8000moo`8mkbQoo`0000=oocg_Ool057oo0P0047oo00Ool2?Nl[Ool00003Oolmkgoo015oo`8000moo`8m kbeoo`0000=oocg_Ool03goo0P003goo0Sg_;goo00000goo?Nmoo`0=Ool2000@Ool00cg_Oomoo`0_ Ool00003Oolmkgoo00aoo`03001oogoo00ioo`8mkc9oo`0000=oocg_Ool02Woo0P003goo0Sg_=7oo 00000goo?Nmoo`08Ool2000?Ool2?NlfOol00003Oolmkgoo00Moo`03001oogoo00ioo`03?Nmoogoo 03Ioo`0000=oocg_Ool05Woo0Sg_>Goo00000goo?Nmoo`0DOol2?NlkOol00003Oolmkgoo01=oo`03 ?Nmoogoo03]oo`0000=oocg_Ool04Goo0Sg_?Woo00000goo?Nmoo`0?Ool2?Nm0Ool00003Oolmkgoo 00eoo`8mkd9oo`0000=oocg_Ool037oo00"], ImageRangeCache->{{{0, 83.375}, {96.4375, 0}} -> {-0.806251, -1.36632, 0.0283359, 0.0283359}}] }, Open ]], Cell[TextData[{ "We next define a function to display the array of all Bell lists. In this \ case, it is more difficult to decide how to partition the graphics arrays \ because there are no simple divisors of the numbers of Bell lists. A \ technique that works for the arrays that we're likely to want to see is to \ factor the number of elements in the array, and then partition the array into \ rows whose length is equal to the largest prime divisor of the number of \ elements. (This technique fails for the 877 partitions in ", StyleBox["BellLists[7]", "Input"], ", but even we have our limits.)" }], "Text"], Cell[BoxData[ \(PartitionGraphArray[ L_List /; \((PrimeQ[Length[L]] || Length[L] == 1)\)] := L\)], "Input"], Cell[BoxData[ \(PartitionGraphArray[L_List] := Partition[L, First[Last[FactorInteger[Length[L]]]]]\)], "Input"], Cell[TextData[{ "Here is our ", StyleBox["ShowBellDiagrams", "Input"], " function." }], "Text"], Cell[BoxData[ \(ShowBellDiagrams[n_Integer /; n > 2] := Show@\(GraphicsArray@ \(PartitionGraphArray@Map[BellDiagram, BellLists[n]]\)\)\)], "Input"], Cell["\<\ Here are the diagrams corresponding to the third, fourth, and fifth \ Bell numbers.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(ShowBellDiagrams[3]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .21383 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.190476 0.00509127 0.190476 [ [ 0 0 0 0 ] [ 1 .21383 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .21383 L 0 .21383 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.00509127 0.200176 0.208742 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.34127 0.42328 0.57735 0.42328 [ [ 0 0 0 0 ] [ 1 1.1547 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.1547 L 0 1.1547 L closepath clip newpath .5 g .5 Mabswid .97619 .57735 m .02381 1.12721 L .02381 .02749 L .97619 .57735 L s 0 g .76455 .57735 m .76455 .57735 L s .12963 .94392 m .12963 .94392 L s .12963 .21078 m .12963 .21078 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.217813 0.00509127 0.39418 0.208742 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.34127 0.42328 0.57735 0.42328 [ [ 0 0 0 0 ] [ 1 1.1547 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.1547 L 0 1.1547 L closepath clip newpath .5 g .5 Mabswid .97619 .57735 m .02381 1.12721 L .02381 .02749 L .97619 .57735 L s 0 g .76455 .57735 m .12963 .94392 L .76455 .57735 L s .12963 .21078 m .12963 .21078 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.411817 0.00509127 0.588183 0.208742 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.34127 0.42328 0.57735 0.42328 [ [ 0 0 0 0 ] [ 1 1.1547 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.1547 L 0 1.1547 L closepath clip newpath .5 g .5 Mabswid .97619 .57735 m .02381 1.12721 L .02381 .02749 L .97619 .57735 L s 0 g .76455 .57735 m .12963 .21078 L .76455 .57735 L s .12963 .94392 m .12963 .94392 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.60582 0.00509127 0.782187 0.208742 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.34127 0.42328 0.57735 0.42328 [ [ 0 0 0 0 ] [ 1 1.1547 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.1547 L 0 1.1547 L closepath clip newpath .5 g .5 Mabswid .97619 .57735 m .02381 1.12721 L .02381 .02749 L .97619 .57735 L s 0 g .76455 .57735 m .76455 .57735 L s .12963 .94392 m .12963 .21078 L .12963 .94392 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.799824 0.00509127 0.97619 0.208742 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.34127 0.42328 0.57735 0.42328 [ [ 0 0 0 0 ] [ 1 1.1547 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.1547 L 0 1.1547 L closepath clip newpath .5 g .5 Mabswid .97619 .57735 m .02381 1.12721 L .02381 .02749 L .97619 .57735 L s 0 g .76455 .57735 m .12963 .94392 L .12963 .21078 L .76455 .57735 L s MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 61.5625}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHg7oo0009Ool3?NldOol3?NldOol3?NldOol3?NldOol3?NlhOol000Uoo`03?Nmo ogoo008mkc9oo`03?Nmoogoo008mkc9oo`03?Nmoogoo008mkc9oo`03?Nmoogoo008mkc9oo`03?Nmo ogoo008mkcIoo`002Goo00Ool2?NlTOol00cg_Oomoo`0>Ool2?NlTOol00cg_ Oomoo`03Ool20009Ool2?NlTOol00cg_Oomoo`02Ool00`00Oomoo`09Ool2?NlTOol00cg_Oomoo`02 Ool30009Ool2?NlXOol000Uoo`03?Nmoogoo011oo`8mkb9oo`03?Nmoogoo011oo`8mkb9oo`03?Nmo ogoo00Eoo`8000Uoo`8mkb9oo`03?Nmoogoo009oo`03001oogoo00]oo`8mkb9oo`03?Nmoogoo009o o`03001oogoo008000Uoo`8mkbIoo`002Goo00Ool20009Ool2?NlIOol00cg_Oomo o`02Ool00`00Oomoo`0DOol2?NlIOol00cg_Oomoo`02Ool00`00Oomoo`09Ool20009Ool2?NlMOol0 00Uoo`03?Nmoogoo01]oo`8mkaMoo`03?Nmoogoo01]oo`8mkaMoo`03?Nmoogoo011oo`8000Uoo`8m kaMoo`03?Nmoogoo009oo`03001oogoo01Ioo`8mkaMoo`03?Nmoogoo009oo`03001oogoo00]oo`80 00Uoo`8mka]oo`002Goo00 Ool20009Ool2?NlHOol000Uoo`03?Nmoogoo021oo`8mka9oo`03?Nmoogoo021oo`8mka9oo`03?Nmo ogoo01Eoo`8000Uoo`8mka9oo`03?Nmoogoo009oo`03001oogoo01]oo`8mka9oo`03?Nmoogoo009o o`03001oogoo011oo`8000Uoo`8mkaIoo`002Goo007oo0009Ool00cg_Oomoo`0dOol00cg_Oomoo`0dOol00cg_Oomoo`0d Ool00cg_Oomoo`0dOol00cg_Oomoo`0hOol00?moob5oo`00ogoo8Goo0000\ \>"], ImageRangeCache->{{{0, 287}, {60.5625, 0}} -> {-0.159992, -0.0267348, 0.0185366, 0.0185366}, {{8.625, 58.5625}, {59.0625, 1.4375}} -> {-1.21535, -1.43502, 0.0473407, 0.0473407}, {{63.5625, 113.5}, { 59.0625, 1.4375}} -> {-3.81613, -1.43502, 0.0473407, 0.0473407}, {{118.5, 168.438}, {59.0625, 1.4375}} -> {-6.41691, -1.43502, 0.0473407, 0.0473407}, {{173.438, 223.375}, {59.0625, 1.4375}} -> {-9.01769, -1.43502, 0.0473407, 0.0473407}, {{228.375, 278.313}, {59.0625, 1.4375}} -> {-11.6185, -1.43502, 0.0473407, 0.0473407}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Bell4Plot = ShowBellDiagrams[4]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .59259 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.190476 0.0141093 0.190476 [ [ 0 0 0 0 ] [ 1 .59259 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .59259 L 0 .59259 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.0141093 0.200176 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .81746 .5 L s .18254 .5 m .18254 .5 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.217813 0.0141093 0.39418 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .5 .18254 L .81746 .5 L s .18254 .5 m .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.411817 0.0141093 0.588183 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .81746 .5 L s .18254 .5 m .5 .18254 L .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.60582 0.0141093 0.782187 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .18254 .5 L .81746 .5 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.799824 0.0141093 0.97619 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .18254 .5 L .5 .18254 L .81746 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.208113 0.200176 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .18254 .5 L .5 .18254 L .81746 .5 L s .5 .81746 m .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.217813 0.208113 0.39418 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .18254 .5 L .81746 .5 L s .5 .81746 m .5 .18254 L .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.411817 0.208113 0.588183 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .18254 .5 L .5 .81746 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.60582 0.208113 0.782187 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .18254 L .81746 .5 L s .5 .81746 m .18254 .5 L .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.799824 0.208113 0.97619 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .18254 .5 L .5 .18254 L .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.402116 0.200176 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .5 .81746 L s .18254 .5 m .18254 .5 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.217813 0.402116 0.39418 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .18254 L .81746 .5 L s .5 .81746 m .5 .81746 L s .18254 .5 m .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.411817 0.402116 0.588183 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .5 .18254 L .5 .81746 L s .18254 .5 m .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.60582 0.402116 0.782187 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .5 .81746 L s .18254 .5 m .5 .18254 L .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.799824 0.402116 0.97619 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .18254 .5 L .81746 .5 L s .5 .81746 m .5 .81746 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 170.625}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol00cg_Oomoo`0@Ool00`00Oomoo`08Ool0 0`00Oomoo`05Ool00cg_Oomoo`0?Ool00cg_Oomoo`05Ool00`00Oomoo`0KOol00cg_Oomoo`0>Ool0 0cg_Oomoo`0TOol00cg_Oomoo`0>Ool00cg_Oomoo`05Ool00`00Oomoo`0COol00`00Oomoo`05Ool0 0cg_Oomoo`0Ool00`00Oomoo`06Ool00`00Oomoo`05Ool00cg_Oomo o`0COol00cg_Oomoo`0GOol00`00Oomoo`05Ool00cg_Oomoo`0BOol00cg_Oomoo`05Ool00`00Oomo o`0@Ool00`00Oomoo`05Ool00cg_Oomoo`0BOol00cg_Oomoo`05Ool00`00Oomoo`0?Ool00`00Oomo o`05Ool00cg_Oomoo`0>Ool0011oo`03?Nmoogoo01Eoo`03001oogoo00Eoo`03?Nmoogoo01Aoo`03 ?Nmoogoo00eoo`03001oogoo00Eoo`03001oogoo00Eoo`03?Nmoogoo01Eoo`03?Nmoogoo01Eoo`03 001oogoo00Eoo`03?Nmoogoo01Aoo`03?Nmoogoo00Eoo`8000moo`03001oogoo00Eoo`03?Nmoogoo 01Aoo`03?Nmoogoo00Eoo`03001oogoo00eoo`03001oogoo00Eoo`03?Nmoogoo00moo`004Goo00Ool00cg_Oomoo`0@Ool00`00Oomoo`0@ Ool00cg_Oomoo`0?Ool00cg_Oomoo`0SOol00cg_Oomoo`0>Ool00cg_Oomoo`0LOol00`00Oomoo`05 Ool00cg_Oomoo`0>Ool00cg_Oomoo`05Ool00`00Oomoo`08Ool00`00Oomoo`0@Ool00cg_Oomoo`0< Ool000aoo`03?Nmoogoo00Eoo`03001oogoo01Eoo`03001oogoo00Eoo`03?Nmoogoo00aoo`03?Nmo ogoo015oo`03001oogoo015oo`03?Nmoogoo00eoo`03?Nmoogoo02Eoo`03?Nmoogoo00aoo`03?Nmo ogoo01ioo`03001oogoo00Eoo`03?Nmoogoo00aoo`03?Nmoogoo00Eoo`03001oogoo00Uoo`03001o ogoo015oo`03?Nmoogoo00]oo`002goo00 Ool00`00Oomoo`0>Ool00cg_Oomoo`0COol00cg_Oomoo`05Ool00`00Oomoo`0GOol00cg_Oomoo`0B Ool00cg_Oomoo`05Ool00`00Oomoo`0HOol00cg_Oomoo`0BOol00cg_Oomoo`05Ool00`00Oomoo`06 Ool00`00Oomoo`0>Ool00cg_Oomoo`0>Ool0011oo`03?Nmoogoo01eoo`03?Nmoogoo01Aoo`03?Nmo ogoo00eoo`03001oogoo00eoo`03?Nmoogoo01Eoo`03?Nmoogoo00Eoo`03001oogoo01Eoo`03?Nmo ogoo01Aoo`03?Nmoogoo00Eoo`8001Moo`03?Nmoogoo01Aoo`03?Nmoogoo00Eoo`03001oogoo00Eo o`03001oogoo00eoo`03?Nmoogoo00moo`004Goo00Ool00cg_Oomoo`0QOol00cg_Oomoo`0@Ool00cg_Oomoo`0IOol00`00Oomoo`05Ool00cg_Oomo o`0AOol00cg_Oomoo`0?Ool00`00Oomoo`0?Ool00cg_Oomoo`0@Ool00cg_Oomoo`05Ool00`00Oomo o`0JOol00cg_Oomoo`0@Ool00cg_Oomoo`0QOol00cg_Oomoo`0=Ool000eoo`03?Nmoogoo02=oo`03 ?Nmoogoo00ioo`03?Nmoogoo01]oo`03001oogoo00Eoo`03?Nmoogoo00moo`03?Nmoogoo011oo`03 001oogoo011oo`03?Nmoogoo00ioo`03?Nmoogoo00Eoo`03001oogoo01aoo`03?Nmoogoo00ioo`03 ?Nmoogoo02=oo`03?Nmoogoo00aoo`0037oo00Ool00cg_Oomoo`0QOol00cg_Oomoo`0@Ool0 0cg_Oomoo`0QOol00cg_Oomoo`0AOol00cg_Oomoo`0?Ool00`00Oomoo`0?Ool00cg_Oomoo`0@Ool0 0cg_Oomoo`0ROol00cg_Oomoo`0@Ool00cg_Oomoo`0QOol00cg_Oomoo`0=Ool000moo`03?Nmoogoo 01moo`03?Nmoogoo019oo`03?Nmoogoo01moo`03?Nmoogoo01=oo`03?Nmoogoo00ioo`03001oogoo 00ioo`03?Nmoogoo019oo`03?Nmoogoo021oo`03?Nmoogoo019oo`03?Nmoogoo01moo`03?Nmoogoo 00ioo`0047oo00"], ImageRangeCache->{{{0, 287}, {169.625, 0}} -> {-0.131938, -0.0740739, 0.018341, 0.018341}, {{7.1875, 57.625}, {165.563, 115.063}} -> {-2.02389, -1.83067, 0.0624536, 0.0624536}, {{62.6875, 113.188}, {165.563, 115.063}} -> {-5.48522, -1.82841, 0.0623763, 0.0623763}, {{118.25, 168.688}, {165.563, 115.063}} -> {-8.96014, -1.83067, 0.0624536, 0.0624536}, {{173.75, 224.25}, {165.563, 115.063}} -> {-12.4129, -1.82841, 0.0623763, 0.0623763}, {{229.313, 279.75}, {165.563, 115.063}} -> {-15.8964, -1.83067, 0.0624536, 0.0624536}, {{7.1875, 57.625}, {110, 59.5625}} -> {-2.02389, -5.2988, 0.0624536, 0.0624536}, {{62.6875, 113.188}, {110, 59.5625}} -> {-5.49201, -5.2988, 0.0624536, 0.0624536}, {{118.25, 168.688}, {110, 59.5625}} -> {-8.96014, -5.2988, 0.0624536, 0.0624536}, {{ 173.75, 224.25}, {110, 59.5625}} -> {-12.4283, -5.2988, 0.0624536, 0.0624536}, {{229.313, 279.75}, {110, 59.5625}} -> {-15.8964, -5.2988, 0.0624536, 0.0624536}, {{7.1875, 57.625}, {54.5, 4}} -> {-2.02389, -8.76692, 0.0624536, 0.0624536}, {{62.6875, 113.188}, { 54.5, 4}} -> {-5.48522, -8.75607, 0.0623763, 0.0623763}, {{118.25, 168.688}, {54.5, 4}} -> {-8.96014, -8.76692, 0.0624536, 0.0624536}, {{ 173.75, 224.25}, {54.5, 4}} -> {-12.4129, -8.75607, 0.0623763, 0.0623763}, {{229.313, 279.75}, {54.5, 4}} -> {-15.8964, -8.76692, 0.0624536, 0.0624536}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(ShowBellDiagrams[5]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .3184 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.0732601 0.00758097 0.0732601 [ [ 0 0 0 0 ] [ 1 .3184 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .3184 L 0 .3184 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.00758097 0.0908786 0.0781016 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .16578 .31943 L .55818 .19193 L .8007 .52573 L s .16578 .73203 m .16578 .73203 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0975855 0.00758097 0.164655 0.0781016 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .16578 .31943 L .8007 .52573 L s .16578 .73203 m .55818 .19193 L .16578 .73203 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.171362 0.00758097 0.238431 0.0781016 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .55818 .19193 L .8007 .52573 L s .16578 .73203 m .16578 .31943 L .16578 .73203 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.245137 0.00758097 0.312207 0.0781016 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .8007 .52573 L s .16578 .73203 m .16578 .31943 L .55818 .19193 L .16578 .73203 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.318913 0.00758097 0.385983 0.0781016 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .73203 L .16578 .31943 L .55818 .19193 L .8007 .52573 L s .55818 .85953 m .55818 .85953 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.392689 0.00758097 0.459759 0.0781016 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .73203 L .16578 .31943 L .8007 .52573 L s .55818 .85953 m .55818 .19193 L .55818 .85953 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.466465 0.00758097 0.533535 0.0781016 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .73203 L .55818 .19193 L .8007 .52573 L s .55818 .85953 m .16578 .31943 L .55818 .85953 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.540241 0.00758097 0.607311 0.0781016 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .73203 L .8007 .52573 L s .55818 .85953 m .16578 .31943 L .55818 .19193 L .55818 .85953 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.614017 0.00758097 0.681087 0.0781016 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .31943 L .55818 .19193 L .8007 .52573 L s .55818 .85953 m .16578 .73203 L .55818 .85953 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.687793 0.00758097 0.754863 0.0781016 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .31943 L .8007 .52573 L s .55818 .85953 m .16578 .73203 L .55818 .19193 L .55818 .85953 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.761569 0.00758097 0.828638 0.0781016 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .19193 L .8007 .52573 L s .55818 .85953 m .16578 .73203 L .16578 .31943 L .55818 .85953 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.835345 0.00758097 0.902414 0.0781016 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .16578 .73203 L .16578 .31943 L .55818 .19193 L .55818 .85953 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.909121 0.00758097 0.97619 0.0781016 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .16578 .73203 L .16578 .31943 L .55818 .19193 L .8007 .52573 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.0851536 0.0908786 0.155674 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .16578 .73203 L .55818 .19193 L .55818 .85953 L s .16578 .31943 m .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0975855 0.0851536 0.164655 0.155674 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .16578 .73203 L .55818 .85953 L s .16578 .31943 m .55818 .19193 L .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.171362 0.0851536 0.238431 0.155674 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .16578 .73203 L .55818 .19193 L .8007 .52573 L s .16578 .31943 m .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.245137 0.0851536 0.312207 0.155674 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .16578 .73203 L .8007 .52573 L s .16578 .31943 m .55818 .19193 L .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.318913 0.0851536 0.385983 0.155674 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .31943 L .55818 .19193 L .8007 .52573 L s .55818 .85953 m .55818 .85953 L s .16578 .73203 m .16578 .73203 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.392689 0.0851536 0.459759 0.155674 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .31943 L .8007 .52573 L s .55818 .85953 m .55818 .19193 L .55818 .85953 L s .16578 .73203 m .16578 .73203 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.466465 0.0851536 0.533535 0.155674 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .31943 L .8007 .52573 L s .55818 .85953 m .55818 .85953 L s .16578 .73203 m .55818 .19193 L .16578 .73203 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.540241 0.0851536 0.607311 0.155674 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .19193 L .8007 .52573 L s .55818 .85953 m .16578 .31943 L .55818 .85953 L s .16578 .73203 m .16578 .73203 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.614017 0.0851536 0.681087 0.155674 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .16578 .31943 L .55818 .19193 L .55818 .85953 L s .16578 .73203 m .16578 .73203 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.687793 0.0851536 0.754863 0.155674 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .16578 .31943 L .55818 .85953 L s .16578 .73203 m .55818 .19193 L .16578 .73203 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.761569 0.0851536 0.828638 0.155674 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .19193 L .8007 .52573 L s .55818 .85953 m .55818 .85953 L s .16578 .73203 m .16578 .31943 L .16578 .73203 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.835345 0.0851536 0.902414 0.155674 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .55818 .19193 L .55818 .85953 L s .16578 .73203 m .16578 .31943 L .16578 .73203 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.909121 0.0851536 0.97619 0.155674 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .55818 .85953 L s .16578 .73203 m .16578 .31943 L .55818 .19193 L .16578 .73203 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.162726 0.0908786 0.233247 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .16578 .73203 L .16578 .31943 L .55818 .85953 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0975855 0.162726 0.164655 0.233247 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .16578 .73203 L .16578 .31943 L .8007 .52573 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.171362 0.162726 0.238431 0.233247 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .19193 L .8007 .52573 L s .55818 .85953 m .55818 .85953 L s .16578 .73203 m .16578 .73203 L s .16578 .31943 m .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.245137 0.162726 0.312207 0.233247 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .55818 .19193 L .55818 .85953 L s .16578 .73203 m .16578 .73203 L s .16578 .31943 m .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.318913 0.162726 0.385983 0.233247 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .55818 .85953 L s .16578 .73203 m .55818 .19193 L .16578 .73203 L s .16578 .31943 m .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.392689 0.162726 0.459759 0.233247 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .55818 .85953 L s .16578 .73203 m .16578 .73203 L s .16578 .31943 m .55818 .19193 L .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.466465 0.162726 0.533535 0.233247 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .55818 .19193 L .8007 .52573 L s .16578 .73203 m .16578 .73203 L s .16578 .31943 m .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.540241 0.162726 0.607311 0.233247 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .8007 .52573 L s .16578 .73203 m .55818 .19193 L .16578 .73203 L s .16578 .31943 m .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.614017 0.162726 0.681087 0.233247 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .8007 .52573 L s .16578 .73203 m .16578 .73203 L s .16578 .31943 m .55818 .19193 L .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.687793 0.162726 0.754863 0.233247 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .73203 L .55818 .19193 L .8007 .52573 L s .55818 .85953 m .55818 .85953 L s .16578 .31943 m .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.761569 0.162726 0.828638 0.233247 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .73203 L .8007 .52573 L s .55818 .85953 m .55818 .19193 L .55818 .85953 L s .16578 .31943 m .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.835345 0.162726 0.902414 0.233247 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .73203 L .8007 .52573 L s .55818 .85953 m .55818 .85953 L s .16578 .31943 m .55818 .19193 L .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.909121 0.162726 0.97619 0.233247 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .19193 L .8007 .52573 L s .55818 .85953 m .16578 .73203 L .55818 .85953 L s .16578 .31943 m .16578 .31943 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.240299 0.0908786 0.31082 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .55818 .85953 L s .16578 .73203 m .16578 .73203 L s .16578 .31943 m .16578 .31943 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0975855 0.240299 0.164655 0.31082 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .8007 .52573 L s .16578 .73203 m .16578 .73203 L s .16578 .31943 m .16578 .31943 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.171362 0.240299 0.238431 0.31082 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .73203 L .8007 .52573 L s .55818 .85953 m .55818 .85953 L s .16578 .31943 m .16578 .31943 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.245137 0.240299 0.312207 0.31082 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .16578 .73203 L .55818 .85953 L s .16578 .31943 m .16578 .31943 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.318913 0.240299 0.385983 0.31082 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .16578 .73203 L .8007 .52573 L s .16578 .31943 m .16578 .31943 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.392689 0.240299 0.459759 0.31082 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .31943 L .8007 .52573 L s .55818 .85953 m .55818 .85953 L s .16578 .73203 m .16578 .73203 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.466465 0.240299 0.533535 0.31082 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .16578 .31943 L .55818 .85953 L s .16578 .73203 m .16578 .73203 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.540241 0.240299 0.607311 0.31082 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .8007 .52573 L s .55818 .85953 m .55818 .85953 L s .16578 .73203 m .16578 .31943 L .16578 .73203 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.614017 0.240299 0.681087 0.31082 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .16578 .31943 L .8007 .52573 L s .16578 .73203 m .16578 .73203 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.687793 0.240299 0.754863 0.31082 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .55818 .85953 L .8007 .52573 L s .16578 .73203 m .16578 .31943 L .16578 .73203 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.761569 0.240299 0.828638 0.31082 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .73203 L .16578 .31943 L .8007 .52573 L s .55818 .85953 m .55818 .85953 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.835345 0.240299 0.902414 0.31082 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .73203 L .8007 .52573 L s .55818 .85953 m .16578 .31943 L .55818 .85953 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.909121 0.240299 0.97619 0.31082 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.449727 0.350975 0.525731 0.350975 [ [ 0 0 0 0 ] [ 1 1.05146 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1.05146 L 0 1.05146 L closepath clip newpath .5 g .5 Mabswid .97619 .52573 m .61241 1.02643 L .02381 .83518 L .02381 .21628 L .61241 .02503 L .97619 .52573 L s 0 g .8007 .52573 m .16578 .31943 L .8007 .52573 L s .55818 .85953 m .16578 .73203 L .55818 .85953 L s .55818 .19193 m .55818 .19193 L s MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{445, 141.625}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol00`00Oomoo`02Ool00cg_Oomoo`05Ool013g_Oomoogoo 0P002Woo00<007ooOol01Goo00 Ool00`00Oomoo`03Ool00cg_Oomoo`06Ool00cg_Oomoo`0DOol00cg_Oomoo`07Ool00cg_Oomoo`0= Ool00`00Oomoo`04Ool00cg_Oomoo`06Ool00cg_Oomoo`0;Ool00`00Oomoo`07Ool00cg_Oomoo`06 Ool00cg_Oomoo`0;Ool00`00Ool00006Ool00cg_Oomoo`07Ool00cg_Oomoo`03Ool3000>Ool00cg_ Oomoo`06Ool00cg_Oomoo`03Ool30007Ool00`00Oomoo`04Ool00cg_Oomoo`07Ool00cg_Oomoo`03 Ool30005Ool00`00Oomoo`06Ool00cg_Oomoo`06Ool00cg_Oomoo`03Ool30007Ool00`00Oomoo`04 Ool00cg_Oomoo`07Ool00cg_Oomoo`03Ool30009Ool00`00Oomoo`02Ool00cg_Oomoo`0@Ool000ao o`03?Nmoogoo00aoo`03001oo`0000Aoo`03?Nmoogoo00Moo`03?Nmoogoo00aoo`03001oo`0000Eo o`03?Nmoogoo00Moo`03?Nmoogoo00eoo`8000Aoo`03?Nmoogoo00Qoo`03?Nmoogoo00ioo`03001o ogoo009oo`03?Nmoogoo00Moo`03?Nmoogoo01Aoo`03?Nmoogoo00Moo`03?Nmoogoo00eoo`03001o ogoo00=oo`03?Nmoogoo00Moo`03?Nmoogoo00aoo`03001oogoo00Eoo`03?Nmoogoo00Moo`03?Nmo ogoo00aoo`8000Eoo`03?Nmoogoo00Qoo`03?Nmoogoo00Ioo`8000]oo`03?Nmoogoo00Moo`03?Nmo ogoo00Ioo`<000Aoo`03001oogoo00Aoo`03?Nmoogoo00Moo`03?Nmoogoo00Ioo`<000=oo`03001o ogoo00Aoo`03?Nmoogoo00Moo`03?Nmoogoo00Ioo`<000Aoo`03001oogoo00Aoo`03?Nmoogoo00Mo o`03?Nmoogoo00Ioo`<000Eoo`03001oogoo009oo`03?Nmoogoo015oo`0037oo0Sg_3Goo00<007oo 00000goo00Ool3?Nl=Ool00cg_Oomoo`0>Ool3?NlOol3?Nl=Ool00cg_Oomoo`0>Ool3?NlOol3?Nl=Ool00cg_Oomoo`0> Ool3?NlOol3?Nl=Ool00cg_Oomoo`0>Ool3?Nl< Ool00cg_Oomoo`0>Ool3?Nl=Ool00cg_Oomoo`0>Ool3?NlOol3?Nl=Ool00cg_Oomoo`0>Ool3?NlOol3?Nl=Ool00cg_Oomoo`0>Ool3?NlOol3?Nl=Ool00cg_Oomo o`0>Ool3?NlOol3?Nl=Ool00cg_Oomoo`0>Ool3 ?NlOol3?Nl=Ool00cg_Oomoo`0>Ool3?NlOol00`00Oomoo`03Ool00cg_Oomoo`08Ool2?Nl:Ool40005Ool00cg_Oomoo`0B Ool000aoo`03?Nmoogoo00]oo`03001oo`0000Eoo`03?Nmoogoo00Moo`03?Nmoogoo00Moo`8000]o o`03?Nmoogoo00Moo`03?Nmoogoo00]oo`04001oogoo0004Ool00cg_Oomoo`08Ool00cg_Oomoo`06 Ool2000;Ool00cg_Oomoo`07Ool00cg_Oomoo`06Ool30005Ool00`00Oomoo`03Ool00cg_Oomoo`07 Ool00cg_Oomoo`0=Ool00`00Oomoo`03Ool00cg_Oomoo`07Ool00cg_Oomoo`0Ool00`00Oomoo`02Ool00cg_Oomoo`08Ool00cg_Oomoo`06 Ool20004Ool00`00Oomoo`04Ool00cg_Oomoo`07Ool00cg_Oomoo`0;Ool00`00Oomoo`06Ool00cg_ Oomoo`07Ool00cg_Oomoo`0>Ool00`00Oomoo`02Ool00cg_Oomoo`07Ool00cg_Oomoo`0=Ool00`00 Oomoo`04Ool00cg_Oomoo`07Ool00cg_Oomoo`06Ool30002Ool00`00Oomoo`05Ool00cg_Oomoo`0A Ool000aoo`03?Nmoogoo00]oo`03001oo`0000Ioo`03?Nmoogoo00Ioo`03?Nmoogoo00Aoo`<000io o`03?Nmoogoo00Ioo`03?Nmoogoo00]oo`05001oogooOol00004Ool00cg_Oomoo`07Ool00cg_Oomo o`03Ool3000>Ool00cg_Oomoo`06Ool00cg_Oomoo`03Ool30009Ool00`00Oomoo`02Ool00cg_Oomo o`07Ool00cg_Oomoo`0=Ool00`00Oomoo`04Ool00cg_Oomoo`06Ool00cg_Oomoo`0;Ool00`00Oomo o`07Ool00cg_Oomoo`06Ool00cg_Oomoo`0?Ool00`00Oomoo`02Ool00cg_Oomoo`07Ool00cg_Oomo o`03Ool30006Ool00`00Oomoo`05Ool00cg_Oomoo`06Ool00cg_Oomoo`0;Ool00`00Oomoo`06Ool0 0cg_Oomoo`07Ool00cg_Oomoo`0?Ool00`00Oomoo`02Ool00cg_Oomoo`06Ool00cg_Oomoo`0=Ool0 0`00Oomoo`04Ool00cg_Oomoo`07Ool00cg_Oomoo`03Ool30005Ool00`00Oomoo`06Ool00cg_Oomo o`0@Ool000aoo`05?NmoogooOol00008Ool01000Oomoo`001goo00Ool0 0`00Oomoo`02Ool00cg_Oomoo`06Ool013g_Oomoogoo0P002Goo00<007ooOol01Woo00Ool0 0`00Oomoo`02Ool00cg_Oomoo`05Ool01Cg_Oomoogoo00002goo00<007ooOol01Goo00Ool00cg_Oomoo`0Ool00cg_Oomoo`03Ool00cg_Oomoo`07Ool00`00Oomoo`02Ool00`00Oomoo`09 Ool00cg_Oomoo`02Ool00cg_Oomoo`04Ool01000Oomoo`0047oo00Ool0 0`00Oomoo`02Ool00cg_Oomoo`08Ool2?NlDOol00cg_Oomoo`08Ool2?Nl=Ool00`00Oomoo`03Ool0 0cg_Oomoo`09Ool2?NlOol00`00Oomoo`03Ool00cg_Oomoo`08Ool2?NlCOol0 0cg_Oomoo`0BOol000ioo`Ool4?Nl:Ool01@00Oomoogoo?Nl03Goo 13g_2goo00D007ooOomoocg_00eoo`@mk`Yoo`05001oogooOolmk`0>Ool4?Nl9Ool00`00Oomoo`02 Ool00cg_Oomoo`0;Ool4?Nl:Ool00`00Oomoo`02Ool00cg_Oomoo`0;Ool4?Nl9Ool20003Ool00cg_ Oomoo`0;Ool4?Nl:Ool00`00Oomoo`02Ool00cg_Oomoo`0;Ool4?Nl:Ool01@00Oomoogoo?Nl03Woo 13g_27oo0P0017oo00Ool20004Ool00cg_Oomoo`08Ool2?Nl=Ool0 0`00Oomoo`03Ool00cg_Oomoo`09Ool2?Nl9Ool30007Ool00cg_Oomoo`08Ool2?Nl=Ool00`00Ool0 0004Ool00cg_Oomoo`08Ool2?Nl>Ool00`00Oomoo`02Ool00cg_Oomoo`08Ool2?Nl:Ool30007Ool0 0cg_Oomoo`08Ool2?Nl?Ool01@00Oomoogoo?Nl057oo000Ool00`00Oomoo`02Ool00cg_Oomoo`08 Ool00cg_Oomoo`0Ool00cg_Oomoo`06Ool00cg_Oomoo`0= Ool00`00Ool00005Ool00cg_Oomoo`06Ool00cg_Oomoo`0;Ool00`00Oomoo`06Ool00cg_Oomoo`07 Ool00cg_Oomoo`03Ool3000>Ool00cg_Oomoo`06Ool00cg_Oomoo`0;Ool01@00Oomoogoo000017oo 00Ool000aoo`07?NmoogooOol007oo 00004goo00Ool000aoo`05?NmoogooOol00007Ool0 0`00Oomoo`09Ool00cg_Oomoo`05Ool00cg_Oomoo`02Ool00`00Oomoo`0;Ool00`00Oomoo`03Ool0 0cg_Oomoo`05Ool00cg_Oomoo`0EOol00cg_Oomoo`06Ool00cg_Oomoo`0Ool01@00Oomoogoo?Nl02goo00Ool00`00Oomoo`02Ool00cg_Oomoo`0;Ool3?Nl:Ool00`00Oomoo`03 Ool00cg_Oomoo`08Ool2?Nl>Ool00`00Oomoo`02Ool00cg_Oomoo`09Ool2?Nl>Ool00`00Oomoo`02 Ool00cg_Oomoo`08Ool2?Nl>Ool00`00Oomoo`03Ool00cg_Oomoo`08Ool2?Nl>Ool00`00Oomoo`02 Ool00cg_Oomoo`09Ool2?Nl=Ool00`00Oomoo`03Ool00cg_Oomoo`08Ool2?Nl>Ool00`00Oomoo`02 Ool00cg_Oomoo`09Ool2?Nl>Ool00`00Oomoo`02Ool00cg_Oomoo`08Ool2?Nl>Ool00`00Oomoo`02 Ool00cg_Oomoo`09Ool2?Nl=Ool20004Ool00cg_Oomoo`0BOol000ioo`@mk`ioo`03?Nmoogoo00]o o`@mk`moo`03?Nmoogoo00]oo`@mk`ioo`03?Nmoogoo00moo` Ool4?Nl:Ool01@00Oomoogoo?Nl03Goo13g_2Woo00<007ooOol00Woo00Ool30005Ool00cg_Oomoo`02 Ool00cg_Oomoo`05Ool00`00Oomoo`0@Ool00cg_Oomoo`03Ool00cg_Oomoo`0@Ool30005Ool00cg_ Oomoo`0Ool30005Ool00cg_Oomoo`02Ool00cg_Oomoo`06Ool00`00Oomoo`07 Ool30005Ool00cg_Oomoo`03Ool00cg_Oomoo`0HOol00cg_Oomoo`0Ool000aoo`05?NmoogooOol0000COol00cg_Oomoo`05Ool00cg_Oomoo`02Ool00`00 Oomoo`0;Ool00`00Oomoo`03Ool00cg_Oomoo`05Ool00cg_Oomoo`03Ool3000?Ool00cg_Oomoo`06 Ool00cg_Oomoo`0EOol00cg_Oomoo`05Ool00cg_Oomoo`03Ool3000:Ool00`00Oomoo`02Ool00cg_ Oomoo`06Ool01Cg_Oomoogoo00004goo00Ool00`00Oomoo`03Ool0 0cg_Oomoo`07Ool00cg_Oomoo`0COol00cg_Oomoo`08Ool00cg_Oomoo`07Ool40008Ool00cg_Oomo o`07Ool00cg_Oomoo`06Ool30005Ool00`00Oomoo`02Ool00cg_Oomoo`08Ool00cg_Oomoo`0COol0 0cg_Oomoo`07Ool00cg_Oomoo`0Ool00`00Oomoo`02Ool00cg_Oomoo`08Ool2?Nl?Ool00`00Oomoo`02Ool00cg_Oomoo`08Ool2 ?Nl>Ool00`00Oomoo`02Ool00cg_Oomoo`09Ool2?NlOol00`00Oomoo`02Ool00cg_Oomoo`08Ool2 ?Nl=Ool00`00Oomoo`04Ool00cg_Oomoo`08Ool2?Nl>Ool00`00Oomoo`02Ool00cg_Oomoo`09Ool2 ?NlOol00`00Oomoo`02Ool00cg_Oomoo`08Ool2?Nl=Ool00`00Oomoo`04Ool00cg_Oomoo`08Ool2 ?Nl:Ool30006Ool00cg_Oomoo`0BOol000ioo`@mk`ioo`03?Nmoogoo00]oo`@mk`Yoo`03001oogoo 009oo`03?Nmoogoo00]oo`@mk`ioo`03?Nmoogoo00aoo`@mk`ioo`03?Nmoogoo00]oo`@mk`Uoo`80 00Aoo`03?Nmoogoo00]oo`@mk`ioo`03?Nmoogoo00]oo`@mk`Yoo`03001oogoo009oo`03?Nmoogoo 00]oo`@mk`ioo`03?Nmoogoo00aoo`@mk`Uoo`03001oogoo009oo`03?Nmoogoo00]oo`@mk`Yoo`03 001oogoo009oo`03?Nmoogoo00]oo`@mk`ioo`03?Nmoogoo00]oo`@mk`Yoo`03001oogoo009oo`03 ?Nmoogoo00]oo`@mk`Uoo`8000=oo`03?Nmoogoo01=oo`004Woo0cg_2Woo00"], ImageRangeCache->{{{0, 444}, {140.625, 0}} -> {-0.361137, -0.10348, 0.030906, 0.030906}, {{11.625, 41.25}, {137.25, 106.125}} -> {-2.40141, -1.82276, 0.0962514, 0.0962514}, {{44.25, 73.875}, { 137.25, 106.125}} -> {-5.54161, -1.82276, 0.0962514, 0.0962514}, {{76.8125, 106.438}, {137.25, 106.125}} -> {-8.6758, -1.82276, 0.0962514, 0.0962514}, {{109.438, 139}, {137.25, 106.125}} -> {-11.8288, -1.82518, 0.096379, 0.096379}, {{142, 171.625}, {137.25, 106.125}} -> {-14.9502, -1.82276, 0.0962514, 0.0962514}, {{174.563, 204.188}, {137.25, 106.125}} -> {-18.0844, -1.82276, 0.0962514, 0.0962514}, {{207.188, 236.813}, {137.25, 106.125}} -> {-21.2246, -1.82276, 0.0962514, 0.0962514}, {{239.75, 269.375}, {137.25, 106.125}} -> {-24.3588, -1.82276, 0.0962514, 0.0962514}, {{272.313, 301.938}, {137.25, 106.125}} -> {-27.493, -1.82276, 0.0962514, 0.0962514}, {{304.938, 334.563}, {137.25, 106.125}} -> {-30.6332, -1.82276, 0.0962514, 0.0962514}, {{337.5, 367.125}, {137.25, 106.125}} -> {-33.7673, -1.82276, 0.0962514, 0.0962514}, {{370.063, 399.688}, {137.25, 106.125}} -> {-36.9015, -1.82276, 0.0962514, 0.0962514}, {{402.688, 432.313}, {137.25, 106.125}} -> {-40.0417, -1.82276, 0.0962514, 0.0962514}, {{11.625, 41.25}, {103, 71.8125}} -> {-2.39941, -5.11835, 0.0961757, 0.0961757}, {{44.25, 73.875}, { 103, 71.8125}} -> {-5.53714, -5.11835, 0.0961757, 0.0961757}, {{76.8125, 106.438}, {103, 71.8125}} -> {-8.66886, -5.11835, 0.0961757, 0.0961757}, {{ 109.438, 139}, {103, 71.8125}} -> {-11.8288, -5.12918, 0.096379, 0.096379}, {{142, 171.625}, {103, 71.8125}} -> {-14.9383, -5.11835, 0.0961757, 0.0961757}, {{174.563, 204.188}, {103, 71.8125}} -> {-18.07, -5.11835, 0.0961757, 0.0961757}, {{207.188, 236.813}, {103, 71.8125}} -> {-21.2078, -5.11835, 0.0961757, 0.0961757}, {{ 239.75, 269.375}, {103, 71.8125}} -> {-24.3395, -5.11835, 0.0961757, 0.0961757}, {{272.313, 301.938}, {103, 71.8125}} -> {-27.4712, -5.11835, 0.0961757, 0.0961757}, {{304.938, 334.563}, {103, 71.8125}} -> {-30.6089, -5.11835, 0.0961757, 0.0961757}, {{337.5, 367.125}, {103, 71.8125}} -> {-33.7407, -5.11835, 0.0961757, 0.0961757}, {{ 370.063, 399.688}, {103, 71.8125}} -> {-36.8724, -5.11835, 0.0961757, 0.0961757}, {{402.688, 432.313}, {103, 71.8125}} -> {-40.0101, -5.11835, 0.0961757, 0.0961757}, {{11.625, 41.25}, {68.75, 37.5625}} -> {-2.39941, -8.41237, 0.0961757, 0.0961757}, {{44.25, 73.875}, { 68.75, 37.5625}} -> {-5.53714, -8.41237, 0.0961757, 0.0961757}, {{76.8125, 106.438}, {68.75, 37.5625}} -> {-8.66886, -8.41237, 0.0961757, 0.0961757}, {{109.438, 139}, {68.75, 37.5625}} -> {-11.8288, -8.43016, 0.096379, 0.096379}, {{142, 171.625}, {68.75, 37.5625}} -> {-14.9383, -8.41237, 0.0961757, 0.0961757}, {{174.563, 204.188}, {68.75, 37.5625}} -> {-18.07, -8.41237, 0.0961757, 0.0961757}, {{ 207.188, 236.813}, {68.75, 37.5625}} -> {-21.2078, -8.41237, 0.0961757, 0.0961757}, {{239.75, 269.375}, {68.75, 37.5625}} -> {-24.3395, -8.41237, 0.0961757, 0.0961757}, {{272.313, 301.938}, {68.75, 37.5625}} -> {-27.4712, -8.41237, 0.0961757, 0.0961757}, {{304.938, 334.563}, {68.75, 37.5625}} -> {-30.6089, -8.41237, 0.0961757, 0.0961757}, {{337.5, 367.125}, {68.75, 37.5625}} -> {-33.7407, -8.41237, 0.0961757, 0.0961757}, {{370.063, 399.688}, {68.75, 37.5625}} -> {-36.8724, -8.41237, 0.0961757, 0.0961757}, {{402.688, 432.313}, {68.75, 37.5625}} -> {-40.0101, -8.41237, 0.0961757, 0.0961757}, {{11.625, 41.25}, {34.4375, 3.3125}} -> {-2.40141, -11.7186, 0.0962514, 0.0962514}, {{44.25, 73.875}, {34.4375, 3.3125}} -> {-5.54161, -11.7186, 0.0962514, 0.0962514}, {{76.8125, 106.438}, {34.4375, 3.3125}} -> {-8.6758, -11.7186, 0.0962514, 0.0962514}, {{109.438, 139}, {34.4375, 3.3125}} -> {-11.8288, -11.7342, 0.096379, 0.096379}, {{142, 171.625}, {34.4375, 3.3125}} -> {-14.9502, -11.7186, 0.0962514, 0.0962514}, {{174.563, 204.188}, {34.4375, 3.3125}} -> {-18.0844, -11.7186, 0.0962514, 0.0962514}, {{207.188, 236.813}, {34.4375, 3.3125}} -> {-21.2246, -11.7186, 0.0962514, 0.0962514}, {{239.75, 269.375}, {34.4375, 3.3125}} -> {-24.3588, -11.7186, 0.0962514, 0.0962514}, {{272.313, 301.938}, {34.4375, 3.3125}} -> {-27.493, -11.7186, 0.0962514, 0.0962514}, {{304.938, 334.563}, {34.4375, 3.3125}} -> {-30.6332, -11.7186, 0.0962514, 0.0962514}, {{337.5, 367.125}, {34.4375, 3.3125}} -> {-33.7673, -11.7186, 0.0962514, 0.0962514}, {{370.063, 399.688}, {34.4375, 3.3125}} -> {-36.9015, -11.7186, 0.0962514, 0.0962514}, {{402.688, 432.313}, {34.4375, 3.3125}} -> {-40.0417, -11.7186, 0.0962514, 0.0962514}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Stirling set numbers", "Section"], Cell[TextData[{ "The Stirling set numbers (often called ", StyleBox["Stirling numbers of the second kind", FontSlant->"Italic"], ", denoted ", Cell[BoxData[ FormBox[ RowBox[{ StyleBox["{", SpanMaxSize->Infinity], StyleBox[GridBox[{ {"n"}, {"k"} }], SpanMaxSize->Infinity, FontSize->10], StyleBox["}", SpanMaxSize->Infinity]}], TraditionalForm]]], ") describe the number of ways a set with ", StyleBox["n", FontSlant->"Italic"], " elements can be partitioned into ", StyleBox["k", FontSlant->"Italic"], " disjoint, non-empty subsets. For example, the set ", Cell[BoxData[ \(TraditionalForm\`{1, 2, 3}\)]], " can be partitioned into three subsets in one way \[LongDash] ", Cell[BoxData[ \(TraditionalForm\`{{1}, {2}, {3}}\)]], " \[LongDash] into two subsets in the following three ways \[LongDash] ", Cell[BoxData[ \(TraditionalForm\`{{1, 2}, {3}}, \ {{1, 3}, {2}}\)]], ", and ", Cell[BoxData[ \(TraditionalForm\`{{1}, {2, 3}}\)]], " \[LongDash] and into one subset in the following way \[LongDash] ", Cell[BoxData[ \(TraditionalForm\`{{1, 2, 3}}\)]], ". (The ", Cell[BoxData[ \(TraditionalForm\`n\^th\)]], " Bell number is thus the sum of the ", Cell[BoxData[ \(TraditionalForm\`\((n, k)\)\^th\)]], " Stirling set numbers for ", Cell[BoxData[ \(TraditionalForm\`k = 1, 2, \[Ellipsis], n\)]], ".)" }], "Text"], Cell[TextData[{ "To recursively generate the Stirling set numbers, we use a technique \ similar to that used for generating Bell numbers: for a given list of \ partitions of ", Cell[BoxData[ \(TraditionalForm\`n - 1\)]], " elements, we add the singleton ", Cell[BoxData[ \(TraditionalForm\`{n}\)]], " to the partitions making up ", Cell[BoxData[ FormBox[ RowBox[{ StyleBox["{", SpanMaxSize->Infinity], StyleBox[GridBox[{ {\(n - 1\)}, {\(k - 1\)} }], SpanMaxSize->Infinity, FontSize->10], StyleBox["}", SpanMaxSize->Infinity]}], TraditionalForm]]], ", and add the element ", Cell[BoxData[ \(TraditionalForm\`n\)]], " to each list in the partitions making up ", Cell[BoxData[ FormBox[ RowBox[{"{", StyleBox[GridBox[{ {\(n - 1\)}, {"k"} }], FontSize->10], "}"}], TraditionalForm]]], ". Here are the ", StyleBox["Mathematica", FontSlant->"Italic"], " translations of the two methods." }], "Text"], Cell[BoxData[ \(StirlingSetRule1[n_] = {S__} \[Rule] {S, {n}}; \n StirlingSetRule2[n_] = {b___, {S__}, a___} \[Rule] {b, {S, n}, a}; \)], "Input"], Cell[TextData[ "In this case, we give two \[OpenCurlyDoubleQuote]boundary conditions\ \[CloseCurlyDoubleQuote]."], "Text"], Cell[BoxData[ \(StirlingSetLists[n_Integer?NonNegative, 1] := {{Range[n]}}\)], "Input"], Cell[BoxData[ \(StirlingSetLists[n_Integer?NonNegative, n_] := {Partition[Range[n], 1]} \)], "Input"], Cell[BoxData[ \(StirlingSetLists[n_, k_] := \(StirlingSetLists[n, k] = \n\t\t Flatten[Join[\n\t\t\t Map[ReplaceList[#, StirlingSetRule1[n]]&, StirlingSetLists[n - 1, k - 1]], \n\t\t\t Map[ReplaceList[#, StirlingSetRule2[n]]&, StirlingSetLists[n - 1, k]]], 1]\)\)], "Input"], Cell[TextData[{ "Here are the partitions corresponding to ", Cell[BoxData[ FormBox[ RowBox[{"{", StyleBox[GridBox[{ {"4"}, {"2"} }], FontSize->10], "}"}], TraditionalForm]], SpanMaxSize->Infinity], "." }], "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(StirlingSetLists[4, 2] // ColumnForm\)], "Input"], Cell[BoxData[ InterpretationBox[GridBox[{ {\({{1, 2, 3}, {4}}\)}, {\({{1, 2, 4}, {3}}\)}, {\({{1, 2}, {3, 4}}\)}, {\({{1, 3, 4}, {2}}\)}, {\({{1, 3}, {2, 4}}\)}, {\({{1, 4}, {2, 3}}\)}, {\({{1}, {2, 3, 4}}\)} }, GridBaseline->{Baseline, {1, 1}}, ColumnAlignments->{Left}], ColumnForm[ {{{1, 2, 3}, {4}}, {{1, 2, 4}, {3}}, {{1, 2}, {3, 4}}, {{1, 3, 4}, {2}}, {{1, 3}, {2, 4}}, {{1, 4}, {2, 3}}, {{1}, {2, 3, 4}}}], Editable->False]], "Output"] }, Open ]], Cell["\<\ The functions for displaying a single Stirling number of the second \ kind diagram and for displaying the entire array are nearly identical to the \ code for displaying the Bell list diagrams.\ \>", "Text"], Cell[BoxData[ \(StirlingSetDiagram[L_List] := Module[{thisPoly = Poly[Max[L]], frm}, frm = {GrayLevel[0.5], Line[1.5 thisPoly]}; Graphics[{frm, Map[Loop, Map[thisPoly\[LeftDoubleBracket]#\[RightDoubleBracket]&, L]]}]] \)], "Input"], Cell[BoxData[ \(ShowStirlingSetDiagrams[n_, k_] := Show[GraphicsArray[ PartitionGraphArray[ Map[StirlingSetDiagram, StirlingSetLists[n, k]]]]]\)], "Input"], Cell["Here are our diagrams.", "Text"], Cell[CellGroupData[{ Cell[BoxData[ \(\(ShowStirlingSetDiagrams[4, 1]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.0238095 0.952381 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.0238095 0.97619 0.97619 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .18254 .5 L .5 .18254 L .81746 .5 L s MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{72, 72}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol000ioo`03?Nmoogoo00Qoo`03001oogoo015oo`03001oogoo00Qoo`03?Nmoogoo 00eoo`003Goo00Ool0011oo`03?Nmoogoo00Qoo`03001oogoo00eoo`03001oogoo 00Qoo`03?Nmoogoo00moo`004Goo00"], ImageRangeCache->{{{0, 71}, {71, 0}} -> {-0.0250052, -0.0250052, 0.0147889, 0.0147889}, {{1.6875, 69.25}, {69.25, 1.6875}} -> {-1.6537, -1.65661, 0.046624, 0.046624}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(ShowStirlingSetDiagrams[4, 2]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .13158 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.136054 0.00313283 0.136054 [ [ 0 0 0 0 ] [ 1 .13158 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .13158 L 0 .13158 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.00313283 0.149123 0.128446 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .18254 .5 L .81746 .5 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.161654 0.00313283 0.286967 0.128446 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .5 .18254 L .81746 .5 L s .18254 .5 m .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.299499 0.00313283 0.424812 0.128446 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .81746 .5 L s .18254 .5 m .5 .18254 L .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.437343 0.00313283 0.562657 0.128446 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .18254 .5 L .5 .18254 L .81746 .5 L s .5 .81746 m .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.575188 0.00313283 0.700501 0.128446 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .18254 .5 L .81746 .5 L s .5 .81746 m .5 .18254 L .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.713033 0.00313283 0.838346 0.128446 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .18254 L .81746 .5 L s .5 .81746 m .18254 .5 L .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.850877 0.00313283 0.97619 0.128446 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .18254 .5 L .5 .18254 L .5 .81746 L s MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{288, 37.875}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol00`00Oomoo`03Ool00cg_Oomo o`0Ool000ioo`03 ?Nmoogoo01Moo`03?Nmoogoo00Yoo`03?Nmoogoo00Yoo`03001oogoo00Aoo`03001oogoo009oo`03 ?Nmoogoo00]oo`03?Nmoogoo009oo`03001oogoo015oo`03?Nmoogoo00Yoo`03?Nmoogoo00=oo`03 001oogoo00]oo`03001oogoo00=oo`03?Nmoogoo00Yoo`03?Nmoogoo00Yoo`03001oogoo00Uoo`03 ?Nmoogoo00]oo`03?Nmoogoo011oo`03001oogoo00=oo`03?Nmoogoo00Yoo`03?Nmoogoo00=oo`03 001oogoo00Aoo`03001oogoo00Yoo`03?Nmoogoo00eoo`003Goo00Ool00cg_ Oomoo`03Ool00`00Oomoo`0;Ool00`00Oomoo`03Ool00cg_Oomoo`0:Ool00cg_Oomoo`0:Ool00`00 Oomoo`04Ool00`00Oomoo`02Ool00cg_Oomoo`0;Ool00cg_Oomoo`0@Ool00`00Oomoo`03Ool00cg_ Oomoo`0:Ool00cg_Oomoo`0GOol00cg_Oomoo`0:Ool00cg_Oomoo`0:Ool00`00Oomoo`09Ool00cg_ Oomoo`0;Ool00cg_Oomoo`02Ool00`00Oomoo`0AOol00cg_Oomoo`0:Ool00cg_Oomoo`03Ool00`00 Oomoo`04Ool00`00Oomoo`0:Ool00cg_Oomoo`0=Ool000moo`03?Nmoogoo00=oo`03001oogoo00Uo o`03001oogoo00=oo`03?Nmoogoo00aoo`03?Nmoogoo00Uoo`03001oogoo00=oo`03001oogoo009o o`03?Nmoogoo00eoo`03?Nmoogoo00ioo`03001oogoo00=oo`03?Nmoogoo00aoo`03?Nmoogoo01Eo o`03?Nmoogoo00aoo`03?Nmoogoo00Uoo`03001oogoo00Qoo`03?Nmoogoo00eoo`03?Nmoogoo009o o`03001oogoo00moo`03?Nmoogoo00aoo`03?Nmoogoo00=oo`03001oogoo00=oo`03001oogoo00Uo o`03?Nmoogoo00ioo`0047oo00"], ImageRangeCache->{{{0, 287}, {36.875, 0}} -> {-0.263545, -0.0230264, 0.0262269, 0.0262269}, {{10, 45.125}, {35.9375, 0.875}} -> {-2.47623, -1.65924, 0.0898406, 0.0898406}, {{48.625, 83.75}, { 35.9375, 0.875}} -> {-5.94632, -1.65924, 0.0898406, 0.0898406}, {{87.25, 122.375}, {35.9375, 0.875}} -> {-9.41641, -1.65924, 0.0898406, 0.0898406}, {{125.938, 161}, {35.9375, 0.875}} -> {-12.8893, -1.65924, 0.0898406, 0.0898406}, {{164.563, 199.688}, {35.9375, 0.875}} -> {-16.3622, -1.65924, 0.0898406, 0.0898406}, {{203.188, 238.313}, {35.9375, 0.875}} -> {-19.8323, -1.65924, 0.0898406, 0.0898406}, {{241.813, 276.938}, {35.9375, 0.875}} -> {-23.3024, -1.65924, 0.0898406, 0.0898406}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(ShowStirlingSetDiagrams[4, 3]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .65625 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.31746 0.015625 0.31746 [ [ 0 0 0 0 ] [ 1 .65625 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .65625 L 0 .65625 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.015625 0.321429 0.313244 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .18254 L .81746 .5 L s .5 .81746 m .5 .81746 L s .18254 .5 m .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.35119 0.015625 0.64881 0.313244 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .5 .18254 L .5 .81746 L s .18254 .5 m .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.678571 0.015625 0.97619 0.313244 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .5 .81746 L s .18254 .5 m .5 .18254 L .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.343006 0.321429 0.640625 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .81746 .5 L s .18254 .5 m .18254 .5 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.35119 0.343006 0.64881 0.640625 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .18254 .5 L .81746 .5 L s .5 .81746 m .5 .81746 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.678571 0.343006 0.97619 0.640625 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .18254 .5 L .5 .81746 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{139.313, 91.375}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol00cg_Oomoo`0:Ool00`00Oomoo`04Ool00cg_Oomoo`0FOol00cg_Oomoo`07Ool00`00 Oomoo`07Ool00cg_Oomoo`0FOol00cg_Oomoo`04Ool00`00Oomoo`0:Ool00cg_Oomoo`0Ool00cg_ Oomoo`07Ool00cg_Oomoo`0POol00cg_Oomoo`05Ool000Moo`03?Nmoogoo01ioo`03?Nmoogoo00Uo o`03?Nmoogoo00ioo`03001oogoo00eoo`03?Nmoogoo00Uoo`03?Nmoogoo01ioo`03?Nmoogoo00Io o`0027oo00Ool0015oo`03?Nmoogoo00]oo`03?Nmoogoo 01aoo`03?Nmoogoo00Aoo`03001oogoo00Aoo`03?Nmoogoo01aoo`03?Nmoogoo00]oo`03?Nmoogoo 00moo`004Woo00Ool00cg_Oomoo`0AOol00cg_Oomoo`0FOol00cg_Oomoo`0AOol0 0cg_Oomoo`0FOol00cg_Oomoo`0AOol00cg_Oomoo`0Ool00`00Oomoo`03Ool00cg_Oomoo`0COol00cg_Oomoo`0DOol0 0cg_Oomoo`0COol00cg_Oomoo`04Ool00`00Oomoo`0=Ool00cg_Oomoo`0;Ool000eoo`03?Nmoogoo 00aoo`03001oogoo00=oo`03?Nmoogoo01Eoo`03?Nmoogoo019oo`03?Nmoogoo01Eoo`03?Nmoogoo 00Aoo`03001oogoo00]oo`03?Nmoogoo00aoo`003Woo0Sg_2goo00<007ooOol00goo00Ool0015oo`03?Nmoogoo00Eoo`03001oogoo00=o o`03?Nmoogoo01aoo`03?Nmoogoo00]oo`03?Nmoogoo01aoo`03?Nmoogoo00=oo`03001oogoo00Eo o`03?Nmoogoo00moo`004Woo00"], ImageRangeCache->{{{0, 138.313}, {90.375, 0}} -> {-0.0818416, -0.0492188, 0.0228735, 0.0228735}, {{3.5625, 44.5625}, {88.1875, 47.1875}} -> {-1.84871, -1.74307, 0.0768293, 0.0768293}, {{48.625, 89.625}, {88.1875, 47.1875}} -> {-5.31083, -1.74307, 0.0768293, 0.0768293}, {{93.6875, 134.688}, {88.1875, 47.1875}} -> {-8.77295, -1.74307, 0.0768293, 0.0768293}, {{3.5625, 44.5625}, {43.125, 2.125}} -> {-1.84871, -5.20519, 0.0768293, 0.0768293}, {{ 48.625, 89.625}, {43.125, 2.125}} -> {-5.31083, -5.20519, 0.0768293, 0.0768293}, {{93.6875, 134.688}, {43.125, 2.125}} -> {-8.77295, -5.20519, 0.0768293, 0.0768293}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(ShowStirlingSetDiagrams[4, 4]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: 1 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.952381 0.0238095 0.952381 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.0238095 0.97619 0.97619 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .5 .81746 L s .18254 .5 m .18254 .5 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{74, 74}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgOol00cg_Oomoo`0YOol00cg_Oomoo`0=Ool000eoo`03 ?Nmoogoo02]oo`03?Nmoogoo00aoo`0037oo00Goo00Goo00"], ImageRangeCache->{{{0, 73}, {73, 0}} -> {-0.0250052, -0.0250052, 0.0143837, 0.0143837}, {{1.6875, 71.25}, {71.25, 1.6875}} -> {-1.65143, -1.65426, 0.0452835, 0.0452835}}] }, Open ]], Cell[TextData[{ "As we can see, ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{\(\[Sum]\+n\), RowBox[{"{", StyleBox[GridBox[{ {"4"}, {"n"} }], FontSize->10], "}"}]}], "=", \(B\_4\)}], TraditionalForm]]], "." }], "Text"], Cell[BoxData[ \(\(S4kLists = Flatten[Map[StirlingSetLists[4, #]&, {1, 2, 3, 4}], 1]; \)\)], "Input"], Cell[BoxData[ \(\(S4kPlot = GraphicsArray[ Partition[Reverse[Map[StirlingSetDiagram, S4kLists]], 5]]; \)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(Show[GraphicsArray[{Bell4Plot, S4kPlot}]]; \)\)], "Input"], Cell[GraphicsData["PostScript", "\<\ %! %%Creator: Mathematica %%AspectRatio: .28219 MathPictureStart /Mabs { Mgmatrix idtransform Mtmatrix dtransform } bind def /Mabsadd { Mabs 3 -1 roll add 3 1 roll add exch } bind def %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.47619 0.00671874 0.47619 [ [ 0 0 0 0 ] [ 1 .28219 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .28219 L 0 .28219 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.00671874 0.477324 0.275468 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.190476 0.0141093 0.190476 [ [ 0 0 0 0 ] [ 1 .59259 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .59259 L 0 .59259 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.0141093 0.200176 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .81746 .5 L s .18254 .5 m .18254 .5 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.217813 0.0141093 0.39418 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .5 .18254 L .81746 .5 L s .18254 .5 m .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.411817 0.0141093 0.588183 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .81746 .5 L s .18254 .5 m .5 .18254 L .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.60582 0.0141093 0.782187 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .18254 .5 L .81746 .5 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.799824 0.0141093 0.97619 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .18254 .5 L .5 .18254 L .81746 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.208113 0.200176 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .18254 .5 L .5 .18254 L .81746 .5 L s .5 .81746 m .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.217813 0.208113 0.39418 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .18254 .5 L .81746 .5 L s .5 .81746 m .5 .18254 L .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.411817 0.208113 0.588183 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .18254 .5 L .5 .81746 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.60582 0.208113 0.782187 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .18254 L .81746 .5 L s .5 .81746 m .18254 .5 L .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.799824 0.208113 0.97619 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .18254 .5 L .5 .18254 L .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.402116 0.200176 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .5 .81746 L s .18254 .5 m .18254 .5 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.217813 0.402116 0.39418 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .18254 L .81746 .5 L s .5 .81746 m .5 .81746 L s .18254 .5 m .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.411817 0.402116 0.588183 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .5 .18254 L .5 .81746 L s .18254 .5 m .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.60582 0.402116 0.782187 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .5 .81746 L s .18254 .5 m .5 .18254 L .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.799824 0.402116 0.97619 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .18254 .5 L .81746 .5 L s .5 .81746 m .5 .81746 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.522676 0.00671874 0.97619 0.275468 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.0238095 0.190476 0.0141093 0.190476 [ [ 0 0 0 0 ] [ 1 .59259 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 .59259 L 0 .59259 L closepath clip newpath % Start of sub-graphic p 0.0238095 0.0141093 0.200176 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .18254 .5 L .5 .18254 L .81746 .5 L s .5 .81746 m .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.217813 0.0141093 0.39418 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .81746 .5 L s .18254 .5 m .5 .18254 L .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.411817 0.0141093 0.588183 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .5 .18254 L .81746 .5 L s .18254 .5 m .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.60582 0.0141093 0.782187 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .18254 .5 L .81746 .5 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.799824 0.0141093 0.97619 0.190476 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .18254 .5 L .5 .18254 L .81746 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.208113 0.200176 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .18254 .5 L .81746 .5 L s .5 .81746 m .5 .81746 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.217813 0.208113 0.39418 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .81746 L .81746 .5 L s .18254 .5 m .18254 .5 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.411817 0.208113 0.588183 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .18254 .5 L .5 .18254 L .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.60582 0.208113 0.782187 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .18254 L .81746 .5 L s .5 .81746 m .18254 .5 L .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.799824 0.208113 0.97619 0.38448 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .18254 .5 L .81746 .5 L s .5 .81746 m .5 .18254 L .5 .81746 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.0238095 0.402116 0.200176 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .5 .81746 L s .18254 .5 m .18254 .5 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.217813 0.402116 0.39418 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .5 .81746 L s .18254 .5 m .5 .18254 L .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.411817 0.402116 0.588183 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .5 .18254 L .5 .81746 L s .18254 .5 m .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.60582 0.402116 0.782187 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .5 .18254 L .81746 .5 L s .5 .81746 m .5 .81746 L s .18254 .5 m .18254 .5 L s MathSubEnd P % End of sub-graphic % Start of sub-graphic p 0.799824 0.402116 0.97619 0.578483 MathSubStart %% Graphics %%IncludeResource: font Courier %%IncludeFont: Courier /Courier findfont 10 scalefont setfont % Scaling calculations 0.5 0.31746 0.5 0.31746 [ [ 0 0 0 0 ] [ 1 1 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath 0 0 m 1 0 L 1 1 L 0 1 L closepath clip newpath .5 g .5 Mabswid .97619 .5 m .5 .97619 L .02381 .5 L .5 .02381 L .97619 .5 L s 0 g .81746 .5 m .81746 .5 L s .5 .81746 m .18254 .5 L .5 .81746 L s .5 .18254 m .5 .18254 L s MathSubEnd P % End of sub-graphic MathSubEnd P % End of sub-graphic % End of Graphics MathPictureEnd \ \>"], "Graphics", ImageSize->{417, 117.563}, ImageMargins->{{43, 0}, {0, 0}}, ImageRegion->{{0, 1}, {0, 1}}, ImageCache->GraphicsData["Bitmap", "\<\ CF5dJ6E]HGAYHf4PAg9QL6QYHgWoo007oo00DmkgooOomoocg_01moo`05?NmoogooOolmk`0OOol01Cg_Oomoogoo?Nl087oo00Dm kgooOomoocg_01moo`05?NmoogooOolmk`0OOol001eoo`03?Nmoogoo00=oo`03?Nmoogoo01]oo`03 ?Nmoogoo00=oo`03?Nmoogoo01]oo`03?Nmoogoo00=oo`03?Nmoogoo01aoo`03?Nmoogoo00=oo`03 ?Nmoogoo01]oo`03?Nmoogoo00=oo`03?Nmoogoo03Aoo`03?Nmoogoo00=oo`03?Nmoogoo01]oo`03 ?Nmoogoo00=oo`03?Nmoogoo01]oo`03?Nmoogoo00=oo`03?Nmoogoo01aoo`03?Nmoogoo00=oo`03 ?Nmoogoo01]oo`03?Nmoogoo00=oo`03?Nmoogoo01aoo`0077oo00Ool00cg_Oomoo`0@Ool00cg_Oomoo`02 Ool00`00Oomoo`05Ool00`00Oomoo`02Ool00cg_Oomoo`0XOol00cg_Oomoo`02Ool00`00Oomoo`05 Ool01@00Oomoogoo?Nl04Woo00Ool0 0cg_Oomoo`06Ool00`00Oomoo`02Ool00`00Oomoo`02Ool00cg_Oomoo`0>Ool00cg_Oomoo`0AOol0 0cg_Oomoo`0=Ool00cg_Oomoo`02Ool00`00Oomoo`07Ool00`00Oomoo`02Ool00cg_Oomoo`0EOol0 01Eoo`03?Nmoogoo019oo`03?Nmoogoo00aoo`03?Nmoogoo00Qoo`03001oogoo00=oo`03001oogoo 009oo`03?Nmoogoo00aoo`03?Nmoogoo009oo`03001oogoo00eoo`03?Nmoogoo00aoo`03?Nmoogoo 019oo`03?Nmoogoo00aoo`03?Nmoogoo00=oo`03001oogoo00Qoo`03001oogoo009oo`03?Nmoogoo 02Aoo`03?Nmoogoo009oo`03001oogoo00Qoo`03001oogoo009oo`03?Nmoogoo00aoo`03?Nmoogoo 00=oo`03001oogoo00eoo`03?Nmoogoo00aoo`03?Nmoogoo00Moo`03001oogoo00=oo`03001oogoo 009oo`03?Nmoogoo00aoo`03?Nmoogoo01=oo`03?Nmoogoo00]oo`03?Nmoogoo00=oo`03001oogoo 00Qoo`03001oogoo009oo`03?Nmoogoo01Aoo`0057oo00Ool00cg_Oomoo`03Ool00`00Oomo o`05Ool00`00Oomoo`03Ool00cg_Oomoo`0=Ool00cg_Oomoo`03Ool00`00Oomoo`05Ool00`00Oomo o`03Ool00cg_Oomoo`0EOol001Moo`03?Nmoogoo00Uoo`03001oogoo009oo`03?Nmoogoo011oo`03 ?Nmoogoo00Ioo`04001oogoo0005Ool00cg_Oomoo`0@Ool00cg_Oomoo`08Ool00`00Oomoo`03Ool0 0cg_Oomoo`0@Ool00cg_Oomoo`03Ool00`00Oomoo`03Ool00`00Oomoo`02Ool00cg_Oomoo`0@Ool0 0cg_Oomoo`03Ool00`00Oomoo`03Ool00`00Oomoo`03Ool00cg_Oomoo`0XOol00cg_Oomoo`0>Ool0 0cg_Oomoo`0@Ool00cg_Oomoo`09Ool00`00Oomoo`03Ool00cg_Oomoo`0@Ool00cg_Oomoo`05Ool0 1000Oomoo`001Goo00Woo 00Woo007oo00DmkgooOomoocg_01moo`05?NmoogooOolmk`0OOol01Cg_Oomoogoo?Nl087oo 00DmkgooOomoocg_01moo`05?NmoogooOolmk`0OOol001eoo`03?Nmoogoo00=oo`03?Nmoogoo01]o o`03?Nmoogoo00=oo`03?Nmoogoo01]oo`03?Nmoogoo00=oo`03?Nmoogoo01aoo`03?Nmoogoo00=o o`03?Nmoogoo01]oo`03?Nmoogoo00=oo`03?Nmoogoo03Aoo`03?Nmoogoo00=oo`03?Nmoogoo01]o o`03?Nmoogoo00=oo`03?Nmoogoo01]oo`03?Nmoogoo00=oo`03?Nmoogoo01aoo`03?Nmoogoo00=o o`03?Nmoogoo01]oo`03?Nmoogoo00=oo`03?Nmoogoo01aoo`0077oo00Ool00cg_Oomoo`07Ool00`00Oomoo`07Ool00cg_Oomo o`0>Ool00cg_Oomoo`0@Ool00cg_Oomoo`0>Ool00cg_Oomoo`0;Ool00`00Oomoo`02Ool00cg_Oomo o`0>Ool00cg_Oomoo`03Ool01@00Oomoogoo00002Goo00Ool00cg_Oomoo`02Ool0 0`00Oomoo`0Woo00Woo007oo00DmkgooOomoocg_01mo o`05?NmoogooOolmk`0OOol01Cg_Oomoogoo?Nl087oo00DmkgooOomoocg_01moo`05?NmoogooOolm k`0OOol001eoo`03?Nmoogoo00=oo`03?Nmoogoo01]oo`03?Nmoogoo00=oo`03?Nmoogoo01]oo`03 ?Nmoogoo00=oo`03?Nmoogoo01aoo`03?Nmoogoo00=oo`03?Nmoogoo01]oo`03?Nmoogoo00=oo`03 ?Nmoogoo03Aoo`03?Nmoogoo00=oo`03?Nmoogoo01]oo`03?Nmoogoo00=oo`03?Nmoogoo01]oo`03 ?Nmoogoo00=oo`03?Nmoogoo01aoo`03?Nmoogoo00=oo`03?Nmoogoo01]oo`03?Nmoogoo00=oo`03 ?Nmoogoo01aoo`0077oo00Ool00`00Oomoo`02Ool00cg_Oomoo`0Ool00cg_Oomoo`0AOol00cg_ Oomoo`0>Ool00cg_Oomoo`06Ool00`00Oomoo`07Ool00cg_Oomoo`0>Ool00cg_Oomoo`0@Ool00cg_ Oomoo`0>Ool00cg_Oomoo`0AOol00cg_Oomoo`0VOol00cg_Oomoo`0@Ool00cg_Oomoo`0>Ool00cg_ Oomoo`0AOol00cg_Oomoo`0>Ool00cg_Oomoo`06Ool00`00Oomoo`07Ool00cg_Oomoo`0>Ool00cg_ Oomoo`0AOol00cg_Oomoo`0=Ool00cg_Oomoo`03Ool00`00Oomoo`0;Ool00cg_Oomoo`0EOol001Mo o`03?Nmoogoo00ioo`03?Nmoogoo011oo`03?Nmoogoo00moo`03?Nmoogoo011oo`03?Nmoogoo00Eo o`03001oogoo00Ioo`03?Nmoogoo011oo`03?Nmoogoo00ioo`03?Nmoogoo011oo`03?Nmoogoo00mo o`03?Nmoogoo02Qoo`03?Nmoogoo00ioo`03?Nmoogoo011oo`03?Nmoogoo00moo`03?Nmoogoo011o o`03?Nmoogoo00Eoo`03001oogoo00Ioo`03?Nmoogoo011oo`03?Nmoogoo00moo`03?Nmoogoo00mo o`03?Nmoogoo00=oo`03001oogoo00Uoo`03?Nmoogoo01Ioo`0067oo0Sg_3Goo007oo00DmkgooOomoocg_01moo`05?NmoogooOolmk`0OOol01Cg_Oomoogoo?Nl087oo00Dm kgooOomoocg_01moo`05?NmoogooOolmk`0OOol001moo`03?Nmoocg_025oo`03?Nmoocg_025oo`03 ?Nmoocg_029oo`03?Nmoocg_025oo`03?Nmoocg_03Yoo`03?Nmoocg_025oo`03?Nmoocg_025oo`03 ?Nmoocg_029oo`03?Nmoocg_025oo`03?Nmoocg_021oo`0087oo00Woo00"], ImageRangeCache->{{{0, 416}, {116.563, 0}} -> {-0.0574635, -0.0141094, 0.00508396, 0.00508396}, {{11.25, 198.625}, {113.75, 2.75}} -> {-0.441179, -0.152902, 0.0280279, 0.0280279}, {{15.6875, 48.75}, { 111.063, 78.0625}} -> {-3.07546, -2.10002, 0.0954556, 0.0954556}, {{ 52.0625, 85.0625}, {111.063, 78.0625}} -> {-6.54467, -2.10002, 0.0954556, 0.0954556}, {{88.375, 121.438}, {111.063, 78.0625}} -> {-10.0139, -2.10002, 0.0954556, 0.0954556}, {{124.75, 157.75}, {111.063, 78.0625}} -> {-13.4831, -2.10002, 0.0954556, 0.0954556}, {{161.063, 194.125}, {111.063, 78.0625}} -> {-16.9523, -2.10002, 0.0954556, 0.0954556}, {{15.6875, 48.75}, {74.75, 41.6875}} -> {-3.06965, -5.55871, 0.0952751, 0.0952751}, {{52.0625, 85.0625}, {74.75, 41.6875}} -> {-6.54467, -5.56924, 0.0954556, 0.0954556}, {{88.375, 121.438}, {74.75, 41.6875}} -> {-9.99496, -5.55871, 0.0952751, 0.0952751}, {{124.75, 157.75}, {74.75, 41.6875}} -> {-13.4831, -5.56924, 0.0954556, 0.0954556}, {{161.063, 194.125}, {74.75, 41.6875}} -> {-16.9203, -5.55871, 0.0952751, 0.0952751}, {{15.6875, 48.75}, {38.375, 5.375}} -> {-3.07546, -9.03845, 0.0954556, 0.0954556}, {{ 52.0625, 85.0625}, {38.375, 5.375}} -> {-6.54467, -9.03845, 0.0954556, 0.0954556}, {{88.375, 121.438}, {38.375, 5.375}} -> {-10.0139, -9.03845, 0.0954556, 0.0954556}, {{124.75, 157.75}, {38.375, 5.375}} -> {-13.4831, -9.03845, 0.0954556, 0.0954556}, {{161.063, 194.125}, {38.375, 5.375}} -> {-16.9523, -9.03845, 0.0954556, 0.0954556}, {{ 217.313, 404.688}, {113.75, 2.75}} -> {-6.21668, -0.152902, 0.0280279, 0.0280279}, {{221.75, 254.813}, {111.063, 78.0625}} -> {-22.7453, -2.10002, 0.0954556, 0.0954556}, {{258.125, 291.125}, {111.063, 78.0625}} -> {-26.2145, -2.10002, 0.0954556, 0.0954556}, {{294.438, 327.5}, {111.063, 78.0625}} -> {-29.6837, -2.10002, 0.0954556, 0.0954556}, {{330.813, 363.813}, {111.063, 78.0625}} -> {-33.1529, -2.10002, 0.0954556, 0.0954556}, {{367.125, 400.188}, {111.063, 78.0625}} -> {-36.6221, -2.10002, 0.0954556, 0.0954556}, {{221.75, 254.813}, {74.75, 41.6875}} -> {-22.7023, -5.55871, 0.0952751, 0.0952751}, {{258.125, 291.125}, {74.75, 41.6875}} -> {-26.2145, -5.56924, 0.0954556, 0.0954556}, {{294.438, 327.5}, {74.75, 41.6875}} -> {-29.6276, -5.55871, 0.0952751, 0.0952751}, {{ 330.813, 363.813}, {74.75, 41.6875}} -> {-33.1529, -5.56924, 0.0954556, 0.0954556}, {{367.125, 400.188}, {74.75, 41.6875}} -> {-36.5529, -5.55871, 0.0952751, 0.0952751}, {{221.75, 254.813}, {38.375, 5.375}} -> {-22.7453, -9.03845, 0.0954556, 0.0954556}, {{258.125, 291.125}, {38.375, 5.375}} -> {-26.2145, -9.03845, 0.0954556, 0.0954556}, {{ 294.438, 327.5}, {38.375, 5.375}} -> {-29.6837, -9.03845, 0.0954556, 0.0954556}, {{330.813, 363.813}, {38.375, 5.375}} -> {-33.1529, -9.03845, 0.0954556, 0.0954556}, {{367.125, 400.188}, {38.375, 5.375}} -> {-36.6221, -9.03845, 0.0954556, 0.0954556}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Bibliography and related reading", "Section"], Cell[TextData[{ "J. H. Conway and R. K. Guy, ", StyleBox["The Book of Numbers", FontSlant->"Italic"], ". Copernicus (Springer-Verlag), 1996." }], "Text"], Cell[TextData[{ "R. L. Graham, D. E. Knuth, and O. Patashnik, ", StyleBox["Concrete Mathematics: A Foundation for Computer Science", FontSlant->"Italic"], ". Addison-Wesley, 1994." }], "Text"], Cell[TextData[{ "F. S. Roberts, ", StyleBox["Applied Combinatorics", FontSlant->"Italic"], ". Prentice-Hall, 1984." }], "Text"], Cell[TextData[{ "S. Skiena, ", StyleBox[ "Implementing Discrete Mathematics: Combinatorics and Graph Theory with \ Mathematica", FontSlant->"Italic"], ". Addison-Wesley, 1990." }], "Text"], Cell[TextData[{ "E. W. Weisstein, ", StyleBox["CRC Concise Encyclopedia of Mathematics", FontSlant->"Italic"], ". CRC Press, 1998. Portions of the book are currently served from \ http://www.astro.virginia.edu/~eww6n/math/math0.html. This site is the reason \ the Web was invented." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["About the author", "Section"], Cell["\<\ Robert M. Dickau is a former member of technical staff at Wolfram \ Research, and is currently senior technical trainer for InstallShield \ Software Corporation in Schaumburg, Illinois. He holds degrees in mathematics \ and actuarial science from California Polytechnic University and University \ of Illinois at Urbana-Champaign.\ \>", "Text"], Cell[TextData[StyleBox["E-Mail: pops@prairienet.org", "Input", FontWeight->"Plain"]], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["ELECTRONIC SUBSCRIPTIONS", "Section"], Cell[TextData[{ "Included in the distribution for each electronic subscription is the file \ ", StyleBox["VisCombNum.nb", FontFamily->"Courier"], " containing ", StyleBox["Mathematica", FontSlant->"Italic"], " code for the material described in this article." }], "Text"] }, Open ]] }, Open ]] }, FrontEndVersion->"NeXT 3.0", ScreenRectangle->{{0, 1053}, {0, 832}}, ScreenStyleEnvironment->"Working", WindowSize->{779, 685}, WindowMargins->{{Automatic, 97}, {Automatic, 12}}, PageHeaders->{{Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], Inherited, Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"]}, {Cell[ TextData[ {"Combinatorial Enumeration"}], "Header"], Inherited, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"]}}, PrintingOptions->{"FirstPageHeader"->False, "FirstPageFooter"->False}, Magnification->1, StyleDefinitions -> Notebook[{ Cell[CellGroupData[{ Cell["Style Definitions", "Subtitle"], Cell["\<\ Modify the definitions below to change the default appearance of \ all cells in a given style. Make modifications to any definition using \ commands in the Format menu.\ \>", "Text"], Cell[CellGroupData[{ Cell["Style Environment Names", "Section"], Cell[StyleData[All, "Working"], PageWidth->WindowWidth, ScriptMinSize->9], Cell[StyleData[All, "Presentation"], PageWidth->WindowWidth, ScriptMinSize->12, FontSize->16], Cell[StyleData[All, "Condensed"], PageWidth->WindowWidth, CellBracketOptions->{"Margins"->{1, 1}, "Widths"->{0, 5}}, ScriptMinSize->8, FontSize->11], Cell[StyleData[All, "Printout"], PageWidth->PaperWidth, ScriptMinSize->5, FontSize->10, PrivateFontOptions->{"FontType"->"Outline"}] }, Closed]], Cell[CellGroupData[{ Cell["Notebook Options", "Section"], Cell["\<\ The options defined for the style below will be used at the \ Notebook level.\ \>", "Text"], Cell[StyleData["Notebook"], PageHeaders->{{Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"], None, Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"]}, {Cell[ TextData[ { ValueBox[ "FileName"]}], "Header"], None, Cell[ TextData[ { CounterBox[ "Page"]}], "PageNumber"]}}, CellFrameLabelMargins->6, StyleMenuListing->None] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headings", "Section"], Cell[CellGroupData[{ Cell[StyleData["Title"], CellMargins->{{12, Inherited}, {20, 40}}, CellGroupingRules->{"TitleGrouping", 0}, PageBreakBelow->False, CounterIncrements->"Title", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subtitle", 0}, {"Subsubtitle", 0}}, FontFamily->"Helvetica", FontSize->36, FontWeight->"Bold"], Cell[StyleData["Title", "Presentation"], CellMargins->{{24, 10}, {20, 40}}, LineSpacing->{1, 0}, FontSize->44], Cell[StyleData["Title", "Condensed"], CellMargins->{{8, 10}, {4, 8}}, FontSize->20], Cell[StyleData["Title", "Printout"], CellMargins->{{2, 10}, {15, 30}}, FontSize->24] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subtitle"], CellMargins->{{12, Inherited}, {10, 15}}, CellGroupingRules->{"TitleGrouping", 10}, PageBreakBelow->False, CounterIncrements->"Subtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}, { "Subsubtitle", 0}}, FontFamily->"Helvetica", FontSize->24], Cell[StyleData["Subtitle", "Presentation"], CellMargins->{{24, 10}, {15, 20}}, LineSpacing->{1, 0}, FontSize->36], Cell[StyleData["Subtitle", "Condensed"], CellMargins->{{8, 10}, {4, 4}}, FontSize->14], Cell[StyleData["Subtitle", "Printout"], CellMargins->{{2, 10}, {10, 15}}, FontSize->18] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubtitle"], CellMargins->{{12, Inherited}, {10, 20}}, CellGroupingRules->{"TitleGrouping", 20}, PageBreakBelow->False, CounterIncrements->"Subsubtitle", CounterAssignments->{{"Section", 0}, {"Equation", 0}, {"Figure", 0}}, FontFamily->"Helvetica", FontSize->14, FontSlant->"Italic"], Cell[StyleData["Subsubtitle", "Presentation"], CellMargins->{{24, 10}, {10, 20}}, LineSpacing->{1, 0}, FontSize->24], Cell[StyleData["Subsubtitle", "Condensed"], CellMargins->{{8, 10}, {8, 12}}, FontSize->12], Cell[StyleData["Subsubtitle", "Printout"], CellMargins->{{2, 10}, {8, 10}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Section"], CellDingbat->"\[FilledSquare]", CellMargins->{{25, Inherited}, {8, 24}}, CellGroupingRules->{"SectionGrouping", 30}, PageBreakBelow->False, CounterIncrements->"Section", CounterAssignments->{{"Subsection", 0}, {"Subsubsection", 0}}, FontFamily->"Helvetica", FontSize->16, FontWeight->"Bold"], Cell[StyleData["Section", "Presentation"], CellMargins->{{40, 10}, {11, 32}}, LineSpacing->{1, 0}, FontSize->24], Cell[StyleData["Section", "Condensed"], CellMargins->{{18, Inherited}, {6, 12}}, FontSize->12], Cell[StyleData["Section", "Printout"], CellMargins->{{13, 0}, {7, 22}}, FontSize->14] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsection"], CellDingbat->"\[FilledSmallSquare]", CellMargins->{{22, Inherited}, {8, 20}}, CellGroupingRules->{"SectionGrouping", 40}, PageBreakBelow->False, CounterIncrements->"Subsection", CounterAssignments->{{"Subsubsection", 0}}, FontSize->14, FontWeight->"Bold"], Cell[StyleData["Subsection", "Presentation"], CellMargins->{{36, 10}, {11, 32}}, LineSpacing->{1, 0}, FontSize->22], Cell[StyleData["Subsection", "Condensed"], CellMargins->{{16, Inherited}, {6, 12}}, FontSize->12], Cell[StyleData["Subsection", "Printout"], CellMargins->{{9, 0}, {7, 22}}, FontSize->12] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Subsubsection"], CellDingbat->"\[FilledSmallSquare]", CellMargins->{{22, Inherited}, {8, 18}}, CellGroupingRules->{"SectionGrouping", 50}, PageBreakBelow->False, CounterIncrements->"Subsubsection", FontWeight->"Bold"], Cell[StyleData["Subsubsection", "Presentation"], CellMargins->{{34, 10}, {11, 26}}, LineSpacing->{1, 0}, FontSize->18], Cell[StyleData["Subsubsection", "Condensed"], CellMargins->{{17, Inherited}, {6, 12}}, FontSize->10], Cell[StyleData["Subsubsection", "Printout"], CellMargins->{{9, 0}, {7, 14}}, FontSize->11] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Body Text", "Section"], Cell[CellGroupData[{ Cell[StyleData["Text"], CellMargins->{{12, 10}, {7, 7}}, LineSpacing->{1, 3}, ParagraphIndent->36, CounterIncrements->"Text"], Cell[StyleData["Text", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}], Cell[StyleData["Text", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["Text", "Printout"], CellMargins->{{2, 2}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SmallText"], CellMargins->{{12, 10}, {6, 6}}, LineSpacing->{1, 3}, CounterIncrements->"SmallText", FontFamily->"Helvetica", FontSize->9], Cell[StyleData["SmallText", "Presentation"], CellMargins->{{24, 10}, {8, 8}}, LineSpacing->{1, 5}, FontSize->12], Cell[StyleData["SmallText", "Condensed"], CellMargins->{{8, 10}, {5, 5}}, LineSpacing->{1, 2}, FontSize->9], Cell[StyleData["SmallText", "Printout"], CellMargins->{{2, 2}, {5, 5}}, FontSize->7] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Input/Output", "Section"], Cell["\<\ The cells in this section define styles used for input and output \ to the kernel. Be careful when modifying, renaming, or removing these \ styles, because the front end associates special meanings with these style \ names.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Input"], CellMargins->{{45, 10}, {5, 7}}, Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, CellLabelMargins->{{11, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultInputFormatType, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", FontWeight->"Bold"], Cell[StyleData["Input", "Presentation"], CellMargins->{{72, Inherited}, {8, 10}}, LineSpacing->{1, 0}], Cell[StyleData["Input", "Condensed"], CellMargins->{{40, 10}, {2, 3}}], Cell[StyleData["Input", "Printout"], CellMargins->{{39, 0}, {4, 6}}, FontSize->9] }, Closed]], Cell[StyleData["InputOnly"], Evaluatable->True, CellGroupingRules->"InputGrouping", CellHorizontalScrolling->True, DefaultFormatType->DefaultInputFormatType, AutoItalicWords->{}, FormatType->InputForm, ShowStringCharacters->True, NumberMarks->True, CounterIncrements->"Input", StyleMenuListing->None, FontWeight->"Bold"], Cell[CellGroupData[{ Cell[StyleData["Output"], CellMargins->{{47, 10}, {7, 5}}, CellEditDuplicate->True, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, CellLabelMargins->{{11, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Output"], Cell[StyleData["Output", "Presentation"], CellMargins->{{72, Inherited}, {10, 8}}, LineSpacing->{1, 0}], Cell[StyleData["Output", "Condensed"], CellMargins->{{41, Inherited}, {3, 2}}], Cell[StyleData["Output", "Printout"], CellMargins->{{39, 0}, {6, 4}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Message"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{11, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Message", StyleMenuListing->None, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["Message", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Message", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}], Cell[StyleData["Message", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8, FontColor->GrayLevel[0]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Print"], CellMargins->{{45, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"OutputGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GroupPageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, CellLabelMargins->{{11, Inherited}, {Inherited, Inherited}}, DefaultFormatType->DefaultOutputFormatType, AutoItalicWords->{}, FormatType->InputForm, CounterIncrements->"Print", StyleMenuListing->None], Cell[StyleData["Print", "Presentation"], CellMargins->{{72, Inherited}, {Inherited, Inherited}}, LineSpacing->{1, 0}], Cell[StyleData["Print", "Condensed"], CellMargins->{{41, Inherited}, {Inherited, Inherited}}], Cell[StyleData["Print", "Printout"], CellMargins->{{39, Inherited}, {Inherited, Inherited}}, FontSize->8] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["Graphics"], CellMargins->{{4, Inherited}, {Inherited, Inherited}}, CellGroupingRules->"GraphicsGrouping", CellHorizontalScrolling->True, PageBreakWithin->False, GeneratedCell->True, CellAutoOverwrite->True, ShowCellLabel->False, DefaultFormatType->DefaultOutputFormatType, FormatType->InputForm, CounterIncrements->"Graphics", ImageMargins->{{43, Inherited}, {Inherited, 0}}, StyleMenuListing->None], Cell[StyleData["Graphics", "Presentation"], ImageMargins->{{62, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Condensed"], ImageSize->{175, 175}, ImageMargins->{{38, Inherited}, {Inherited, 0}}], Cell[StyleData["Graphics", "Printout"], ImageSize->{250, 250}, ImageMargins->{{30, Inherited}, {Inherited, 0}}, FontSize->9] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["CellLabel"], StyleMenuListing->None, FontFamily->"Helvetica", FontSize->9, FontColor->RGBColor[0, 0, 1]], Cell[StyleData["CellLabel", "Presentation"], FontSize->12], Cell[StyleData["CellLabel", "Condensed"], FontSize->9], Cell[StyleData["CellLabel", "Printout"], FontFamily->"Courier", FontSize->8, FontSlant->"Italic", FontColor->GrayLevel[0]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Formulas and Programming", "Section"], Cell[CellGroupData[{ Cell[StyleData["InlineFormula"], CellMargins->{{10, 4}, {0, 8}}, CellHorizontalScrolling->True, ScriptLevel->1, SingleLetterItalics->True], Cell[StyleData["InlineFormula", "Presentation"], CellMargins->{{24, 10}, {10, 10}}, LineSpacing->{1, 5}], Cell[StyleData["InlineFormula", "Condensed"], CellMargins->{{8, 10}, {6, 6}}, LineSpacing->{1, 1}], Cell[StyleData["InlineFormula", "Printout"], CellMargins->{{2, 0}, {6, 6}}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["DisplayFormula"], CellMargins->{{42, Inherited}, {Inherited, Inherited}}, CellHorizontalScrolling->True, ScriptLevel->0, SingleLetterItalics->True, StyleMenuListing->None, UnderoverscriptBoxOptions->{LimitsPositioning->True}], Cell[StyleData["DisplayFormula", "Presentation"], LineSpacing->{1, 5}], Cell[StyleData["DisplayFormula", "Condensed"], LineSpacing->{1, 1}], Cell[StyleData["DisplayFormula", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Styles for Headers and Footers", "Section"], Cell[StyleData["Header"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontSize->10, FontSlant->"Italic"], Cell[StyleData["Footer"], CellMargins->{{0, 0}, {0, 4}}, StyleMenuListing->None, FontSize->9, FontSlant->"Italic"], Cell[StyleData["PageNumber"], CellMargins->{{0, 0}, {4, 1}}, StyleMenuListing->None, FontFamily->"Times", FontSize->10] }, Closed]], Cell[CellGroupData[{ Cell["Palette Styles", "Section"], Cell["\<\ The cells below define styles that define standard \ ButtonFunctions, for use in palette buttons.\ \>", "Text"], Cell[StyleData["Paste"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, After]}]&)}], Cell[StyleData["Evaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["EvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionMove[ FrontEnd`InputNotebook[ ], All, Cell, 1], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluate"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluate[ FrontEnd`InputNotebook[ ], All]}]&)}], Cell[StyleData["CopyEvaluateCell"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`SelectionCreateCell[ FrontEnd`InputNotebook[ ], All], FrontEnd`NotebookApply[ FrontEnd`InputNotebook[ ], #, All], FrontEnd`SelectionEvaluateCreateCell[ FrontEnd`InputNotebook[ ], All]}]&)}] }, Closed]], Cell[CellGroupData[{ Cell["Hyperlink Styles", "Section"], Cell["\<\ The cells below define styles useful for making hypertext \ ButtonBoxes. The \"Hyperlink\" style is for links within the same Notebook, \ or between Notebooks.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Hyperlink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`NotebookLocate[ #2]}]&), Active->True, ButtonNote->ButtonData}], Cell[StyleData["Hyperlink", "Presentation"]], Cell[StyleData["Hyperlink", "Condensed"]], Cell[StyleData["Hyperlink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell["\<\ The following styles are for linking automatically to the on-line \ help system.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["MainBookLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "MainBook", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["MainBookLink", "Presentation"]], Cell[StyleData["MainBookLink", "Condensed"]], Cell[StyleData["MainBookLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["AddOnsLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "AddOns", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["AddOnsLink", "Presentation"]], Cell[StyleData["AddOnsLink", "Condensed"]], Cell[StyleData["AddOnLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["RefGuideLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontFamily->"Courier", FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "RefGuideLink", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["RefGuideLink", "Presentation"]], Cell[StyleData["RefGuideLink", "Condensed"]], Cell[StyleData["RefGuideLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["GettingStartedLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "GettingStarted", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["GettingStartedLink", "Presentation"]], Cell[StyleData["GettingStartedLink", "Condensed"]], Cell[StyleData["GettingStartedLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["OtherInformationLink"], StyleMenuListing->None, ButtonStyleMenuListing->Automatic, FontColor->RGBColor[0, 0, 1], FontVariations->{"Underline"->True}, ButtonBoxOptions->{ButtonFunction:>(FrontEndExecute[ { FrontEnd`HelpBrowserLookup[ "OtherInformation", #]}]&), Active->True, ButtonFrame->"None"}], Cell[StyleData["OtherInformationLink", "Presentation"]], Cell[StyleData["OtherInformationLink", "Condensed"]], Cell[StyleData["OtherInformationLink", "Printout"], FontColor->GrayLevel[0], FontVariations->{"Underline"->False}] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["Placeholder Styles", "Section"], Cell["\<\ The cells below define styles useful for making placeholder \ objects in palette templates.\ \>", "Text"], Cell[CellGroupData[{ Cell[StyleData["Placeholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->True, StyleMenuListing->None], Cell[StyleData["Placeholder", "Presentation"]], Cell[StyleData["Placeholder", "Condensed"]], Cell[StyleData["Placeholder", "Printout"]] }, Closed]], Cell[CellGroupData[{ Cell[StyleData["SelectionPlaceholder"], Editable->False, Selectable->False, StyleBoxAutoDelete->True, Placeholder->Primary, StyleMenuListing->None, DrawHighlighted->True], Cell[StyleData["SelectionPlaceholder", "Presentation"]], Cell[StyleData["SelectionPlaceholder", "Condensed"]], Cell[StyleData["SelectionPlaceholder", "Printout"]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell["FormatType Styles", "Section"], Cell["\<\ The cells below define styles that are mixed in with the styles \ of most cells. If a cell's FormatType matches the name of one of the styles \ defined below, then that style is applied between the cell's style and its \ own options.\ \>", "Text"], Cell[StyleData["CellExpression"], PageWidth->Infinity, CellMargins->{{6, Inherited}, {Inherited, Inherited}}, ShowCellLabel->False, ShowSpecialCharacters->False, AllowInlineCells->False, AutoItalicWords->{}, StyleMenuListing->None, FontFamily->"Courier", Background->GrayLevel[1]], Cell[StyleData["InputForm"], AllowInlineCells->False, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["OutputForm"], PageWidth->Infinity, TextAlignment->Left, LineSpacing->{1, -5}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["StandardForm"], LineSpacing->{1.25, 0}, StyleMenuListing->None, FontFamily->"Courier"], Cell[StyleData["TraditionalForm"], LineSpacing->{1.25, 0}, SingleLetterItalics->True, TraditionalFunctionNotation->True, DelimiterMatching->None, StyleMenuListing->None], Cell["\<\ The style defined below is mixed in to any cell that is in an \ inline cell within another.\ \>", "Text"], Cell[StyleData["InlineCell"], TextAlignment->Left, ScriptLevel->1, StyleMenuListing->None], Cell[StyleData["InlineCellEditing"], StyleMenuListing->None, Background->RGBColor[1, 0.749996, 0.8]] }, Closed]] }, Open ]] }] ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. ***********************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1731, 51, 54, 0, 98, "Title"], Cell[1788, 53, 181, 3, 62, "Subsubtitle"], Cell[CellGroupData[{ Cell[1994, 60, 35, 0, 52, "Section"], Cell[2032, 62, 648, 12, 78, "Text"], Cell[CellGroupData[{ Cell[2705, 78, 41, 1, 24, "Input"], Cell[2749, 81, 196, 3, 37, "Output"] }, Open ]], Cell[2960, 87, 395, 8, 62, "Text"], Cell[3358, 97, 410, 7, 62, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[3805, 109, 58, 0, 52, "Section"], Cell[3866, 111, 1614, 46, 110, "Text"], Cell[5483, 159, 282, 7, 46, "Text"], Cell[5768, 168, 275, 7, 46, "Text"], Cell[CellGroupData[{ Cell[6068, 179, 59, 1, 24, "Input"], Cell[6130, 182, 406, 5, 63, "Output"] }, Open ]], Cell[6551, 190, 250, 6, 46, "Text"], Cell[CellGroupData[{ Cell[6826, 200, 64, 1, 25, "Input"], Cell[6893, 203, 177, 4, 24, "Output"] }, Open ]], Cell[7085, 210, 208, 4, 46, "Text"], Cell[7296, 216, 582, 10, 78, "Text"], Cell[7881, 228, 130, 3, 42, "Input"], Cell[8014, 233, 325, 10, 46, "Text"], Cell[8342, 245, 90, 1, 25, "Input"], Cell[8435, 248, 38, 0, 30, "Text"], Cell[CellGroupData[{ Cell[8498, 252, 73, 1, 25, "Input"], Cell[8574, 255, 2886, 73, 64, 633, 41, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[11475, 331, 402, 8, 46, "Text"], Cell[CellGroupData[{ Cell[11902, 343, 62, 1, 24, "Input"], Cell[11967, 346, 58, 1, 24, "Output"] }, Open ]], Cell[12040, 350, 153, 4, 30, "Text"], Cell[CellGroupData[{ Cell[12218, 358, 73, 1, 25, "Input"], Cell[12294, 361, 4362, 96, 50, 731, 47, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[16671, 460, 100, 3, 33, "Text"], Cell[CellGroupData[{ Cell[16796, 467, 106, 2, 30, "Input"], Cell[16905, 471, 6749, 126, 91, 735, 47, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[23669, 600, 349, 10, 52, "Text"], Cell[CellGroupData[{ Cell[24043, 614, 106, 2, 30, "Input"], Cell[24152, 618, 4362, 96, 50, 731, 47, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[28529, 717, 396, 10, 46, "Text"], Cell[28928, 729, 39, 0, 30, "Text"], Cell[CellGroupData[{ Cell[28992, 733, 86, 1, 25, "Input"], Cell[29081, 736, 159, 3, 41, "Output"] }, Open ]], Cell[29255, 742, 703, 20, 78, "Text"], Cell[CellGroupData[{ Cell[29983, 766, 79, 1, 25, "Input"], Cell[30065, 769, 220, 3, 74, "Output"] }, Open ]], Cell[30300, 775, 265, 6, 46, "Text"], Cell[CellGroupData[{ Cell[30590, 785, 56, 1, 25, "Input"], Cell[30649, 788, 4440, 99, 50, 744, 49, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[35104, 890, 126, 5, 30, "Text"], Cell[CellGroupData[{ Cell[35255, 899, 162, 3, 39, "Input"], Cell[35420, 904, 4440, 99, 50, 744, 49, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[39875, 1006, 277, 8, 30, "Text"], Cell[40155, 1016, 917, 28, 78, "Text"], Cell[41075, 1046, 66, 0, 30, "Text"], Cell[41144, 1048, 426, 7, 81, "Input"], Cell[41573, 1057, 106, 3, 30, "Text"], Cell[CellGroupData[{ Cell[41704, 1064, 65, 1, 25, "Input"], Cell[41772, 1067, 8901, 314, 44, 3791, 246, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[50710, 1386, 65, 1, 25, "Input"], Cell[50778, 1389, 31756, 1194, 82, 14447, 972, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[82571, 2588, 65, 1, 25, "Input"], Cell[82639, 2591, 148125, 6118, 231, 75226, 5196, "GraphicsData", "PostScript", "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[230813, 8715, 46, 0, 52, "Section"], Cell[230862, 8717, 564, 13, 71, "Text"], Cell[231429, 8732, 421, 13, 52, "Text"], Cell[231853, 8747, 131, 5, 33, "Text"], Cell[CellGroupData[{ Cell[232009, 8756, 53, 1, 24, "Input"], Cell[232065, 8759, 50, 1, 24, "Output"] }, Open ]], Cell[232130, 8763, 138, 5, 30, "Text"], Cell[CellGroupData[{ Cell[232293, 8772, 56, 1, 24, "Input"], Cell[232352, 8775, 103, 2, 24, "Output"] }, Open ]], Cell[232470, 8780, 948, 34, 62, "Text"], Cell[233421, 8816, 508, 11, 62, "Text"], Cell[233932, 8829, 317, 6, 46, "Text"], Cell[CellGroupData[{ Cell[234274, 8839, 98, 2, 25, "Input"], Cell[234375, 8843, 131, 2, 24, "Output"] }, Open ]], Cell[234521, 8848, 205, 8, 30, "Text"], Cell[234729, 8858, 429, 10, 62, "Text"], Cell[235161, 8870, 91, 1, 24, "Input"], Cell[235255, 8873, 61, 1, 24, "Input"], Cell[235319, 8876, 271, 7, 46, "Text"], Cell[235593, 8885, 199, 4, 39, "Input"], Cell[235795, 8891, 39, 0, 30, "Text"], Cell[CellGroupData[{ Cell[235859, 8895, 48, 1, 24, "Input"], Cell[235910, 8898, 50, 1, 24, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[235997, 8904, 48, 1, 24, "Input"], Cell[236048, 8907, 406, 5, 63, "Output"] }, Open ]], Cell[236469, 8915, 194, 5, 30, "Text"], Cell[CellGroupData[{ Cell[236688, 8924, 70, 1, 24, "Input"], Cell[236761, 8927, 38, 1, 24, "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[236848, 8934, 31, 0, 52, "Section"], Cell[236882, 8936, 515, 11, 62, "Text"], Cell[237400, 8949, 99, 2, 25, "Input"], Cell[237502, 8953, 141, 5, 30, "Text"], Cell[CellGroupData[{ Cell[237668, 8962, 56, 1, 25, "Input"], Cell[237727, 8965, 38, 1, 24, "Output"] }, Open ]], Cell[237780, 8969, 239, 8, 30, "Text"], Cell[CellGroupData[{ Cell[238044, 8981, 56, 1, 25, "Input"], Cell[238103, 8984, 39, 1, 24, "Output"] }, Open ]], Cell[238157, 8988, 152, 3, 30, "Text"], Cell[CellGroupData[{ Cell[238334, 8995, 70, 1, 25, "Input"], Cell[238407, 8998, 56, 1, 24, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[238500, 9004, 70, 1, 25, "Input"], Cell[238573, 9007, 169, 2, 37, "Output"] }, Open ]], Cell[238757, 9012, 289, 6, 46, "Text"], Cell[239049, 9020, 90, 1, 25, "Input"], Cell[239142, 9023, 152, 4, 30, "Text"], Cell[CellGroupData[{ Cell[239319, 9031, 388, 6, 66, "Input"], Cell[239710, 9039, 16050, 519, 126, 5774, 387, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[255775, 9561, 217, 4, 46, "Text"], Cell[255995, 9567, 314, 6, 46, "Text"], Cell[256312, 9575, 110, 2, 42, "Input"], Cell[256425, 9579, 394, 9, 62, "Text"], Cell[256822, 9590, 121, 4, 30, "Text"], Cell[CellGroupData[{ Cell[256968, 9598, 68, 1, 25, "Input"], Cell[257039, 9601, 6618, 122, 171, 714, 45, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[263672, 9726, 519, 12, 62, "Text"], Cell[264194, 9740, 295, 9, 54, "Text"], Cell[264492, 9751, 67, 1, 25, "Input"], Cell[264562, 9754, 102, 2, 25, "Input"], Cell[264667, 9758, 473, 9, 62, "Text"], Cell[CellGroupData[{ Cell[265165, 9771, 446, 8, 39, "Input"], Cell[265614, 9781, 5482, 152, 123, 1578, 99, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[271111, 9936, 151, 3, 30, "Text"], Cell[271265, 9941, 298, 6, 53, "Input"], Cell[271566, 9949, 132, 5, 30, "Text"], Cell[CellGroupData[{ Cell[271723, 9958, 74, 1, 25, "Input"], Cell[271800, 9961, 5520, 154, 123, 1598, 101, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[277335, 10118, 533, 14, 46, "Text"], Cell[277871, 10134, 180, 4, 39, "Input"], Cell[278054, 10140, 127, 5, 30, "Text"], Cell[CellGroupData[{ Cell[278206, 10149, 65, 1, 25, "Input"], Cell[278274, 10152, 31413, 859, 298, 8870, 574, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[309702, 11014, 314, 6, 46, "Text"], Cell[310019, 11022, 343, 6, 53, "Input"], Cell[310365, 11030, 204, 5, 39, "Input"], Cell[CellGroupData[{ Cell[310594, 11039, 65, 1, 25, "Input"], Cell[310662, 11042, 168156, 4555, 232, 56104, 3159, "GraphicsData", "PostScript", "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[478867, 15603, 31, 0, 52, "Section"], Cell[478901, 15605, 322, 9, 46, "Text"], Cell[479226, 15616, 280, 8, 40, "Text"], Cell[479509, 15626, 160, 5, 30, "Text"], Cell[479672, 15633, 482, 14, 88, "Text"], Cell[480157, 15649, 1158, 39, 78, "Text"], Cell[481318, 15690, 135, 5, 30, "Text"], Cell[481456, 15697, 140, 2, 37, "Input"], Cell[481599, 15701, 237, 8, 30, "Text"], Cell[481839, 15711, 66, 1, 24, "Input"], Cell[481908, 15714, 71, 0, 30, "Text"], Cell[CellGroupData[{ Cell[482004, 15718, 71, 1, 25, "Input"], Cell[482078, 15721, 70, 1, 24, "Output"] }, Open ]], Cell[482163, 15725, 76, 0, 30, "Text"], Cell[CellGroupData[{ Cell[482264, 15729, 71, 1, 25, "Input"], Cell[482338, 15732, 81, 1, 24, "Output"] }, Open ]], Cell[482434, 15736, 98, 3, 30, "Text"], Cell[482535, 15741, 61, 1, 24, "Input"], Cell[482599, 15744, 221, 5, 52, "Input"], Cell[482823, 15751, 140, 5, 30, "Text"], Cell[CellGroupData[{ Cell[482988, 15760, 59, 1, 24, "Input"], Cell[483050, 15763, 429, 12, 88, "Output"] }, Open ]], Cell[483494, 15778, 130, 5, 30, "Text"], Cell[CellGroupData[{ Cell[483649, 15787, 59, 1, 24, "Input"], Cell[483711, 15790, 1034, 25, 248, "Output"] }, Open ]], Cell[484760, 15818, 639, 17, 62, "Text"], Cell[485402, 15837, 80, 1, 25, "Input"], Cell[485485, 15840, 290, 7, 39, "Input"], Cell[485778, 15849, 150, 5, 30, "Text"], Cell[CellGroupData[{ Cell[485953, 15858, 71, 1, 25, "Input"], Cell[486027, 15861, 4119, 97, 106, 763, 51, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[490161, 15961, 619, 10, 78, "Text"], Cell[490783, 15973, 119, 2, 25, "Input"], Cell[490905, 15977, 122, 2, 25, "Input"], Cell[491030, 15981, 101, 4, 30, "Text"], Cell[491134, 15987, 168, 3, 39, "Input"], Cell[491305, 15992, 107, 3, 30, "Text"], Cell[CellGroupData[{ Cell[491437, 15999, 58, 1, 25, "Input"], Cell[491498, 16002, 13903, 373, 70, 3592, 241, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[505438, 16380, 70, 1, 25, "Input"], Cell[505511, 16383, 41746, 1106, 179, 9105, 695, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[547294, 17494, 58, 1, 25, "Input"], Cell[547355, 17497, 102877, 3309, 150, 36122, 2470, "GraphicsData", "PostScript", "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[650281, 20812, 39, 0, 52, "Section"], Cell[650323, 20814, 1559, 49, 85, "Text"], Cell[651885, 20865, 1167, 39, 76, "Text"], Cell[653055, 20906, 157, 3, 39, "Input"], Cell[653215, 20911, 122, 2, 30, "Text"], Cell[653340, 20915, 91, 1, 25, "Input"], Cell[653434, 20918, 113, 2, 25, "Input"], Cell[653550, 20922, 346, 7, 66, "Input"], Cell[653899, 20931, 308, 12, 37, "Text"], Cell[CellGroupData[{ Cell[654232, 20947, 69, 1, 25, "Input"], Cell[654304, 20950, 563, 14, 120, "Output"] }, Open ]], Cell[654882, 20967, 216, 4, 46, "Text"], Cell[655101, 20973, 297, 7, 39, "Input"], Cell[655401, 20982, 188, 4, 39, "Input"], Cell[655592, 20988, 38, 0, 30, "Text"], Cell[CellGroupData[{ Cell[655655, 20992, 68, 1, 25, "Input"], Cell[655726, 20995, 5321, 133, 80, 1125, 77, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[661084, 21133, 68, 1, 25, "Input"], Cell[661155, 21136, 16065, 485, 46, 4540, 337, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[677257, 21626, 68, 1, 25, "Input"], Cell[677328, 21629, 14267, 438, 100, 4041, 306, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[CellGroupData[{ Cell[691632, 22072, 68, 1, 25, "Input"], Cell[691703, 22075, 4200, 125, 82, 1167, 83, "GraphicsData", "PostScript", "Graphics"] }, Open ]], Cell[695918, 22203, 349, 13, 37, "Text"], Cell[696270, 22218, 109, 2, 25, "Input"], Cell[696382, 22222, 139, 4, 25, "Input"], Cell[CellGroupData[{ Cell[696546, 22230, 80, 1, 25, "Input"], Cell[696629, 22233, 60506, 1935, 126, 18479, 1406, "GraphicsData", "PostScript", "Graphics"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[757184, 24174, 51, 0, 52, "Section"], Cell[757238, 24176, 163, 5, 30, "Text"], Cell[757404, 24183, 202, 5, 30, "Text"], Cell[757609, 24190, 137, 5, 30, "Text"], Cell[757749, 24197, 200, 7, 30, "Text"], Cell[757952, 24206, 304, 7, 46, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[758293, 24218, 35, 0, 52, "Section"], Cell[758331, 24220, 354, 6, 62, "Text"], Cell[758688, 24228, 95, 1, 28, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[758820, 24234, 43, 0, 52, "Section"], Cell[758866, 24236, 289, 9, 46, "Text"] }, Open ]] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)