PermutationPower
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PermutationPower
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
open allclose allBasic Examples (3)Summary of the most common use cases

https://wolfram.com/xid/0b0kvcg78ou-evspdf

Second power of the inverse permutation:

https://wolfram.com/xid/0b0kvcg78ou-dlxl3

PermutationPower can yield the identity permutation:

https://wolfram.com/xid/0b0kvcg78ou-gp8ts8

Scope (1)Survey of the scope of standard use cases
Generalizations & Extensions (2)Generalized and extended use cases
PermutationPower does not evaluate for symbolic arguments:

https://wolfram.com/xid/0b0kvcg78ou-mqvr0z


https://wolfram.com/xid/0b0kvcg78ou-f3hqhe

PermutationPower performs some simplifications for generic symbolic input:

https://wolfram.com/xid/0b0kvcg78ou-0hrh4p


https://wolfram.com/xid/0b0kvcg78ou-dnta4w

Properties & Relations (1)Properties of the function, and connections to other functions
For exponents that are multiples of the order of the permutation, the permutation power yields identity:

https://wolfram.com/xid/0b0kvcg78ou-nwcn1y

https://wolfram.com/xid/0b0kvcg78ou-wmxxlq

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

https://wolfram.com/xid/0b0kvcg78ou-ckrn90

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.
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.
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
Wolfram Language. (2010). PermutationPower. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PermutationPower.html
BibTeX
@misc{reference.wolfram_2025_permutationpower, author="Wolfram Research", title="{PermutationPower}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PermutationPower.html}", note=[Accessed: 08-July-2025
]}
BibLaTeX
@online{reference.wolfram_2025_permutationpower, organization={Wolfram Research}, title={PermutationPower}, year={2010}, url={https://reference.wolfram.com/language/ref/PermutationPower.html}, note=[Accessed: 08-July-2025
]}