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
open all close allBasic Examples (2)
Scope (2)
Number of integers in the support of a permutation in cyclic form:
PermutationLength[Cycles[{{1, 5, 3, 7}, {2, 6, 10, 8, 4}}]]Length of the support of the identity:
PermutationLength[Cycles[{}]]Number of integers in the support of a permutation list:
PermutationLength[{1, 2, 5, 4, 3, 6, 7}]Length of the support of the identity permutation list:
PermutationLength[{1, 2, 3, 4, 5}]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:
PermutationLength[PermutationGroup[{Cycles[{{1, 3, 5, 7}}], Cycles[{{1, 2}, {3, 4}}]}]]Support length of the default permutation representation of a named abstract group:
PermutationLength[DihedralGroup[5]]Properties & Relations (1)
PermutationLength is equivalent to using Length on the permutation support:
PermutationLength[{1, 4, 3, 10, 2, 6, 5, 7, 9, 8, 11}] === Length@PermutationSupport[{1, 4, 3, 10, 2, 6, 5, 7, 9, 8, 11}]Text
Wolfram Research (2010), PermutationLength, Wolfram Language function, https://reference.wolfram.com/language/ref/PermutationLength.html.
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