This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# PermutationList

 PermutationList[perm] returns a permutation list representation of permutation perm. PermutationListreturns a permutation list of length len.
• The input permutation perm can be given as a permutation list or in disjoint cyclic form.
• For cyclic input Cycles the cycles must be lists of positive integers representing the points of the domain in which the permutation perm acts. The cycles must have no common points.
• PermutationList returns a permutation list that is a reordering of the consecutive integers . By default the length len is the largest integer present in the input perm.
• For an input cycle the resulting permutation list has point at position and at position .
Convert permutation cycles to a permutation list:
Explicit length specification:
Convert permutation cycles to a permutation list:
 Out[1]=

Explicit length specification:
 Out[1]=
 Scope   (3)
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:
The permutation returned by PermutationList[cycs] produces with Part the same result as using the original cycs with Permute:
A simple Mathematica implementation of PermutationList, but which requires the presence of singletons:
PermutationList and PermutationCycles are inverse functions:
PermutationList does not return the list of images of a sorted range of integers:
Use PermutationReplace to compute a list of images:
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:
RELATED DEMONSTRATIONS
New in 8