({{, (RefLink[PermutationSupport, paclet:ref/PermutationSupport])[perm] 
returns the support of the permutation perm.}})

OpenersNotesSection(Spacer1)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.

(RefLink[PermutationSupport, paclet:ref/PermutationSupport]) works with (RefLink[Cycles, paclet:ref/Cycles]) objects as well as with permutation lists. When applied to a permutation list, (RefLink[PermutationSupport, paclet:ref/PermutationSupport])[{(Subscript[p, 1]),…,(Subscript[p, n])}] returns the (Subscript[p, i]) for which (Subscript[p, i])≠i.

OpenersPrimaryExamplesSection(Spacer1)Examples  (7)

OpenersExampleSection0(Spacer1)Basic Examples  (2)

Points moved by a permutation in disjoint cyclic form:

PermutationSupport[Cycles[{{1,7},{2,5,10,9},{4,6}}]]

Points moved in a permutation list:

PermutationSupport[{1,4,3,5,2,6,10,7,9,8}]

OpenersExampleSection1(Spacer1)Scope  (2)

Support of permutations in disjoint cyclic form:

PermutationSupport[Cycles[{{1,8,5},{2,9,4,3}}]]

PermutationSupport[Cycles[{}]]

Support of permutation lists:

PermutationSupport[{5,3,4,9,8,6,7,1,2}]

PermutationSupport[{1,2,3,4,5,6,7,8,9}]

PermutationSupport[{}]

OpenersExampleSection2(Spacer1)Generalizations & Extensions  (1)

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

PermutationSupport[PermutationGroup[{Cycles[{{1,3,5,7}}],Cycles[{{1,2},{3,4}}]}]]

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

PermutationSupport[DihedralGroup[5]]

OpenersExampleSection4(Spacer1)Properties & Relations  (2)

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

PermutationSupport[Cycles[{{2,6},{1,5,3,17}}]]

OrderedQ[%]

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

PermutationSupport[Cycles[{{1,7},{2,5,10,9},{4,6}}]]===Union@@First[Cycles[{{1,7},{2,5,10,9},{4,6}}]]

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[Cycles, paclet:ref/Cycles])  ▪  (RefLink[PermutationMax, paclet:ref/PermutationMax])  ▪  (RefLink[PermutationMin, paclet:ref/PermutationMin])  ▪  (RefLink[PermutationLength, paclet:ref/PermutationLength])}})}})

({{DocumentationFooterIconsRelatedTutorial.png, ({{Tutorials}, {▪(RefLinkPlain[Permutations, paclet:tutorial/Permutations])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Permutations, paclet:guide/Permutations])}})}})