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PermutationPower
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PermutationPower

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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 allclose all

Basic Examples  (3)Summary of the most common use cases

Sixth power of a permutation:

In[1]:=1
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https://wolfram.com/xid/0b0kvcg78ou-evspdf
Out[1]=1

Second power of the inverse permutation:

In[1]:=1
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https://wolfram.com/xid/0b0kvcg78ou-dlxl3
Out[1]=1

PermutationPower can yield the identity permutation:

In[1]:=1
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https://wolfram.com/xid/0b0kvcg78ou-gp8ts8
Out[1]=1

Scope  (1)Survey of the scope of standard use cases

Compute arbitrary powers of a permutation:

In[1]:=1
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https://wolfram.com/xid/0b0kvcg78ou-ima6pi
In[2]:=2
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https://wolfram.com/xid/0b0kvcg78ou-kjj2qp
Out[2]=2

Generalizations & Extensions  (2)Generalized and extended use cases

PermutationPower does not evaluate for symbolic arguments:

In[1]:=1
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https://wolfram.com/xid/0b0kvcg78ou-mqvr0z
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b0kvcg78ou-f3hqhe
Out[2]=2

PermutationPower performs some simplifications for generic symbolic input:

In[1]:=1
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https://wolfram.com/xid/0b0kvcg78ou-0hrh4p
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0b0kvcg78ou-dnta4w
Out[2]=2

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:

In[1]:=1
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https://wolfram.com/xid/0b0kvcg78ou-nwcn1y
In[2]:=2
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https://wolfram.com/xid/0b0kvcg78ou-wmxxlq
Out[2]=2

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

In[3]:=3
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https://wolfram.com/xid/0b0kvcg78ou-ckrn90
Out[3]=3
Wolfram Research (2010), PermutationPower, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationPower.html.
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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.

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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.

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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

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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 ]}

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@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 ]}

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@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 ]}