# InversePermutation

InversePermutation[perm]

returns the inverse of permutation perm.

# Details

• The product of a permutation with its inverse gives the identity permutation.
• Every permutation has a uniquely defined inverse.
• The support of a permutation is the same as the support of its inverse.

# Examples

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## Basic Examples(2)

Inverse of a permutation:

Their product gives the identity permutation:

Some permutations, called involutions, are their own inverse:

## Scope(1)

Invert a permutation:

## Generalizations & Extensions(1)

On symbolic expressions other than permutations the result is given in terms of PermutationPower:

## Properties & Relations(4)

InversePermutation is equivalent to PermutationPower with exponent -1:

Inverting a permutation is equivalent to reversing its cycles:

For a permutation of finite degree, its inverse can always be obtained as the power with a positive integer:

Ordering gives the inverse of a permutation list:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_inversepermutation, author="Wolfram Research", title="{InversePermutation}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/InversePermutation.html}", note=[Accessed: 10-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_inversepermutation, organization={Wolfram Research}, title={InversePermutation}, year={2010}, url={https://reference.wolfram.com/language/ref/InversePermutation.html}, note=[Accessed: 10-September-2024 ]}