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InversePermutation[perm]

returns the inverse of permutation perm.

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Examples  
Basic Examples  
Scope  
Generalizations & Extensions  
Properties & Relations  
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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_2025_inversepermutation, author="Wolfram Research", title="{InversePermutation}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/InversePermutation.html}", note=[Accessed: 11-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_inversepermutation, organization={Wolfram Research}, title={InversePermutation}, year={2010}, url={https://reference.wolfram.com/language/ref/InversePermutation.html}, note=[Accessed: 11-August-2025]}