# PermutationLength

PermutationLength[perm]

returns the number of integers moved by the permutation perm.

# Details • PermutationLength works with Cycles objects as well as with permutation lists.
• The number of integers moved by a permutation is sometimes called its degree. Another common definition of permutation degree is the largest moved point.

# Examples

open allclose all

## Basic Examples(2)

Number of points moved by a permutation:

Number of points moved in a permutation list:

## Scope(2)

Number of integers in the support of a permutation in cyclic form:

Length of the support of the identity:

Number of integers in the support of a permutation list:

Length of the support of the identity permutation list:

## Generalizations & Extensions(1)

The length of the support of a permutation group is defined as the length of the union of the supports of its elements:

Support length of the default permutation representation of a named abstract group:

## Properties & Relations(1)

PermutationLength is equivalent to using Length on the permutation support: