WOLFRAM

Wolfram Language & System Documentation Center

PermutationPower[perm,n]

gives the n^(th) permutation power of the permutation perm.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Generalizations & Extensions  
Properties & Relations  
See Also
Tech Notes
Related Guides
History
Cite this Page

PermutationPower

PermutationPower[perm,n]

gives the n^(th) 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

open all close all

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_2025_permutationpower, author="Wolfram Research", title="{PermutationPower}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PermutationPower.html}", note=[Accessed: 11-August-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: 11-August-2025]}