Permutations are among the most basic elements of discrete mathematics. They can be used to represent discrete groups of transformations and in particular play a key role in the description of the concept of symmetry.
Mathematica 8 provides new functionality to work with permutations, both in list and cyclic form, and allows their action on generic expressions in a variety of ways.
Permutation Representation
Cycles — cyclic permutation representation
PermutationCycles — convert to cyclic representation
PermutationList — convert to permutation list representation
PermutationListQ — test validity
RandomPermutation — random generation of permutations
PermutationReplace — standard action of a permutation on other objects
Permute — permute arguments of an expression
FindPermutation — permutation linking two expressions
Permutations — all permutations of arguments of an expression
PermutationOrder — order of a permutation
Sort — return identity permutation list
Part — product of permutation lists
Ordering — inverse of a permutation list
Signature — signature of a permutation list
RandomSample — random generation of permutation lists
