# PermutationPower

PermutationPower[perm,n]

gives the n permutation power of the permutation perm.

# Details

• PermutationPower[perm,n] effectively computes the product of a permutation perm with itself n times.
• When n is negative, PermutationPower finds powers of the inverse of the permutation perm.
• PermutationPower[perm,0] gives the identity permutation.

# Examples

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## Basic Examples(3)

Sixth power of a permutation:

Second power of the inverse permutation:

PermutationPower can yield the identity permutation:

## Scope(1)

Compute arbitrary powers of a permutation:

## Generalizations & Extensions(2)

PermutationPower does not evaluate for symbolic arguments:

PermutationPower performs some simplifications for generic symbolic input:

## Properties & Relations(1)

For exponents that are multiples of the order of the permutation, the permutation power yields identity:

Hence large powers can be reduced by using the modulo of the exponent:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2023_permutationpower, author="Wolfram Research", title="{PermutationPower}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PermutationPower.html}", note=[Accessed: 04-October-2023 ]}

#### BibLaTeX

@online{reference.wolfram_2023_permutationpower, organization={Wolfram Research}, title={PermutationPower}, year={2010}, url={https://reference.wolfram.com/language/ref/PermutationPower.html}, note=[Accessed: 04-October-2023 ]}