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Multisets Package
Author

David Bevan
Revision date

2011-08-30
Description

The multisets package defines two functions, Multisets and NumberOfMultisets. NumberOfMultisets supports symbolic calculations.
  • Multisets[list, k] gives a list of all multisets containing at most k elements from list.
  • Multisets[list, {k}] gives all multisets containing exactly k elements.
  • Multisets[list, {l, m}] gives all multisets containing between l and m elements.
  • Multisets[list, {l, m, d}] gives all multisets containing l, l + d, ..., m elements.
  • Multisets[list, {{k1, k2, ...}}] gives all multisets containing k1, k2, ... elements.
  • Multisets[list, kspec, m] limits the result to multisets in which the multiplicity of each element is at most m.
  • Multisets[list, kspec, {l, m}] limits the result to multisets in which the multiplicity of each element is between l and m.
  • Multisets[list, kspec, {l, m, d}] limits the result to multisets in which the multiplicity of each element is restricted to l, l + d, ..., m.
  • Multisets[list, kspec, {{m1, m2, ...}}] limits the result to multisets in which the multiplicity of each element is restricted to m1, m2, ....
  • Multisets[list, kspec, mspec, c] limits the result to the first c multisets.
  • NumberOfMultisets[list, kspec] gives the number of multisets of elements of list where the number of elements is specified by kspec.
  • NumberOfMultisets[list, kspec, mspec] gives the number of multisets where the number of elements is specified by kspec and the multiplicities by mspec.
See Multisets for the possible forms for kspec and mspec.

To accompany the multisets package, a notebook containing documentation and examples is also provided.
Subject

*Mathematics > Discrete Mathematics > Combinatorics
Keywords

multiset
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Multisets.m (13.3 KB) - Mathematica Package
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MultisetsDoc.nb (99.5 KB) - Mathematica Notebook