Convert permutation cycles to a permutation list:

Explicit length specification:

Action on cyclic permutations:

The identity permutation can be given as an empty list or as a list of singletons:

On permutation lists the input is returned unchanged:

Pad the permutation list to a different length without changing its support:

PermutationList works efficiently with large inputs:

A simple Wolfram Language implementation of PermutationList, but which requires the presence of singletons:

PermutationList and PermutationCycles are inverse functions:

PermutationList returns the list of images of a sorted range of integers:

The same result can be obtained with the more general function PermutationReplace:

A permutation matrix corresponding to a given disjoint cycle representation:

Use the "PermutationList" property of PermutationMatrix to get the corresponding permutation list:

This is equivalent to directly applying PermutationList to the cycles:

The required length must be equal to or greater than the largest point of the permutation support:

Permutation lists must have machine-sized length:

Illustrate how points get moved under increasing permutations: