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PermutationMin[perm]

returns the smallest integer moved by the permutation perm.

Examples  
Basic Examples  
Scope  
Generalizations & Extensions  
Properties & Relations  
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PermutationMin

PermutationMin[perm]

returns the smallest integer moved by the permutation perm.

Examples

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Basic Examples  (2)

Smallest point moved by a permutation:

Wolfram Language code: PermutationMin[Cycles[{{3, 4, 6}, {2, 7}}]]

Smallest point moved in a permutation list:

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

Scope  (2)

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

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

Minimum of the support of the identity:

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

Smallest integer of the support of a permutation list:

Wolfram Language code: PermutationMin[{1, 2, 5, 4, 3, 6, 7}]

Minimum of the support of the identity permutation list:

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

Generalizations & Extensions  (1)

Smallest integer moved by the elements of a permutation group:

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

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

Wolfram Language code: PermutationMin[DihedralGroup[5]]

Properties & Relations  (2)

On Cycles objects, PermutationMin is equivalent to applying Min:

Wolfram Language code: PermutationMin[Cycles[{{3, 4, 6}, {2, 7}}]] === Min@@Cycles[{{3, 4, 6}, {2, 7}}]

On both Cycles objects and permutation lists, PermutationMin is equivalent to using Min on the permutation support:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_permutationmin, author="Wolfram Research", title="{PermutationMin}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PermutationMin.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_permutationmin, organization={Wolfram Research}, title={PermutationMin}, year={2010}, url={https://reference.wolfram.com/language/ref/PermutationMin.html}, note=[Accessed: 12-June-2026]}