MATHEMATICA GUIDE

# Permutations

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.

## ReferenceReference

### Permutation Representation

Cycles cyclic permutation representation

PermutationCyclesQ test validity

PermutationCycles convert to cyclic representation

PermutationList convert to permutation list representation

PermutationListQ test validity

RandomPermutation random generation of permutations

### Permutation Operations

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

### Permutation Properties

PermutationOrder order of a permutation

### Permutation Lists

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

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