PermutationLength

PermutationLength[perm]

returns the number of integers moved by the permutation perm.

Details

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

Examples

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Basic Examples  (2)

Number of points moved by a permutation:

Number of points moved in a permutation list:

Scope  (2)

Number of integers in the support of a permutation in cyclic form:

Length of the support of the identity:

Number of integers in the support of a permutation list:

Length of the support of the identity permutation list:

Generalizations & Extensions  (1)

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

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

Properties & Relations  (1)

PermutationLength is equivalent to using Length on the permutation support:

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

Text

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

BibTeX

@misc{reference.wolfram_2021_permutationlength, author="Wolfram Research", title="{PermutationLength}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/PermutationLength.html}", note=[Accessed: 23-September-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_permutationlength, organization={Wolfram Research}, title={PermutationLength}, year={2010}, url={https://reference.wolfram.com/language/ref/PermutationLength.html}, note=[Accessed: 23-September-2021 ]}

CMS

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

APA

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