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Implementing Special Numbers: Advanced List Manipulations

Keehong Song
Organization: Pusan National University
Department: Department of Mathematics Education, College of Education
URL: http://www.mathematica.co.kr
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This is a Mathematica Notebook which defines routines for list manipulation that complement those of the Mathematica kernel and the DiscreteMath standard add-on package.

These routines can be valuable in a variety of applications. For example, generating all equivalence relations can be done easily from the Bell partition of the given set, and the triangulations of a convex polygon can be obtained easily from the function CatalanOrder with minor changes. For combinatorial probability problems, these routines are also effective in problem solving. The implementation algorithms are identical to the counting mechanism of the "special numbers." The first two functions, Stirling2nd and Bell are concerned with the partitions of a set while other functions introduced deal with permutations.

*Wolfram Technology > Kernel > Data Structures
*Wolfram Technology > Programming

Bell, Catalan, Derangement, Euler, Recontre, Stirling, Partition, List, Binary tree, cycle
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SpecialNumbers.nb (97.4 KB) - Mathematica notebook