Permutations — list permutations of a set of integers

Permute — permute a list given a permutation

SignaturePermutation — sign or parity of a permutation

IdentityPermutation — identity permutation of a given size

PermutationQ  ▪  LexicographicPermutations  ▪  MinimumChangePermutations

NextPermutation — next permutation in lexicographic ordering

RankPermutation — associate a permutation with a unique rank

InversePermutation  ▪  UnrankPermutation  ▪  RandomPermutation  ▪  Josephus

PermutationType — type of a permutation

PermutationGraph — graph for a permutation

NumberOfPermutationsByType  ▪  NumberOfPermutationsByCycles

SelectionSort — sort a list given an ordering function

BinarySearch — search a sorted list for a key

RandomHeap — construct a random heap

Heapify  ▪  HeapSort

ToInversionVector — inversion vector of a permutation

Inversions — number of inversions

Index — index of a permutation

FromInversionVector  ▪  Runs  ▪  Eulerian

NumberOfPermutationsByInversions

Involutions — list permutations with cycles of length at most 2

Derangements — list permutations leaving no element untouched

InvolutionQ  ▪  NumberOfInvolutions  ▪  DerangementQ  ▪  NumberOfDerangements