# 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

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## 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:

Wolfram Research (2010), PermutationLength, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationLength.html.

#### Text

Wolfram Research (2010), PermutationLength, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationLength.html.

#### CMS

Wolfram Language. 2010. "PermutationLength." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PermutationLength.html.

#### APA

Wolfram Language. (2010). PermutationLength. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PermutationLength.html

#### BibTeX

@misc{reference.wolfram_2022_permutationlength, author="Wolfram Research", title="{PermutationLength}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PermutationLength.html}", note=[Accessed: 10-June-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2022_permutationlength, organization={Wolfram Research}, title={PermutationLength}, year={2010}, url={https://reference.wolfram.com/language/ref/PermutationLength.html}, note=[Accessed: 10-June-2023 ]}