PermutationSupport

PermutationSupport[perm]

returns the support of the permutation perm.

Details

  • The support of a permutation perm is the list of integers that are not fixed by perm.
  • The list of integers is returned sorted.
  • PermutationSupport works with Cycles objects as well as with permutation lists. When applied to a permutation list, PermutationSupport[{p1,…,pn}] returns the pi for which pi≠i.

Examples

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Basic Examples  (2)

Points moved by a permutation in disjoint cyclic form:

Points moved in a permutation list:

Scope  (2)

Support of permutations in disjoint cyclic form:

Support of permutation lists:

Generalizations & Extensions  (1)

The support of a permutation group is defined as the union of the supports of its elements:

Support of the default permutation representation of a named abstract group:

Properties & Relations  (2)

The support of a permutation is returned as an ordered list of integers:

The permutation support of a permutation in cyclic form is the union of its cycles:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2025_permutationsupport, author="Wolfram Research", title="{PermutationSupport}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PermutationSupport.html}", note=[Accessed: 22-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_permutationsupport, organization={Wolfram Research}, title={PermutationSupport}, year={2010}, url={https://reference.wolfram.com/language/ref/PermutationSupport.html}, note=[Accessed: 22-February-2025 ]}