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PermutationMax[perm]

returns the largest integer moved by the permutation perm.

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Examples  
Basic Examples  
Scope  
Generalizations & Extensions  
Properties & Relations  
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PermutationMax

PermutationMax[perm]

returns the largest integer moved by the permutation perm.

Details

  • PermutationMax works with Cycles objects as well as with permutation lists.
  • The largest integer moved by a permutation is sometimes called its degree. Another common definition of permutation degree is the number of integers moved.

Examples

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Basic Examples  (2)

Largest point moved by a permutation:

Wolfram Language code: PermutationMax[Cycles[{{1, 6, 3}, {2, 5, 12, 9}}]]

Largest point moved in a permutation list:

Wolfram Language code: PermutationMax[{1, 4, 3, 10, 2, 6, 5, 7, 9, 8, 11}]

Scope  (2)

Largest integer of the support of a permutation in cyclic form:

Wolfram Language code: PermutationMax[Cycles[{{1, 5, 3, 7}, {2, 6, 10, 8, 4}}]]

Maximum of the support of the identity:

Wolfram Language code: PermutationMax[Cycles[{}]]

Largest integer of the support of a permutation list:

Wolfram Language code: PermutationMax[{7, 4, 5, 8, 1, 2, 3, 10, 9, 6, 11, 12, 13}]

Maximum of the support of the identity permutation list:

Wolfram Language code: PermutationMax[{1, 2, 3, 4, 5}]

Generalizations & Extensions  (1)

Largest integer moved by the elements of a permutation group:

Wolfram Language code: PermutationMax[PermutationGroup[{Cycles[{{1, 3, 5, 7}}], Cycles[{{1, 2}, {3, 4}}]}]]

Largest integer moved by the default permutation representation of a named abstract group:

Wolfram Language code: PermutationLength[DihedralGroup[5]]

Properties & Relations  (2)

On Cycles objects, PermutationMax is equivalent to applying Max:

Wolfram Language code: PermutationMax[Cycles[{{1, 6, 3}, {2, 5, 12, 9}}]] === Max@@Cycles[{{1, 6, 3}, {2, 5, 12, 9}}]

On both Cycles objects and permutation lists, PermutationMax is equivalent to applying Max on the permutation support:

Wolfram Language code: PermutationMax[{1, 4, 3, 10, 2, 6, 5, 7, 9, 8, 11}] === Max@PermutationSupport[{1, 4, 3, 10, 2, 6, 5, 7, 9, 8, 11}]
Wolfram Research (2010), PermutationMax, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationMax.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_permutationmax, author="Wolfram Research", title="{PermutationMax}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PermutationMax.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_permutationmax, organization={Wolfram Research}, title={PermutationMax}, year={2010}, url={https://reference.wolfram.com/language/ref/PermutationMax.html}, note=[Accessed: 13-June-2026]}