({{, (RefLink[PermutationMax, paclet:ref/PermutationMax])[perm] 
returns the largest integer moved by the permutation perm.}})

OpenersNotesSection(Spacer1)Details

(RefLink[PermutationMax, paclet:ref/PermutationMax]) works with (RefLink[Cycles, paclet:ref/Cycles]) objects as well as with permutation lists.

The largest integer moved by a permutation is sometimes called its degree. Another common definition of permutation degree is the number of integers moved.

OpenersPrimaryExamplesSection(Spacer1)Examples  (7)

OpenersExampleSection0(Spacer1)Basic Examples  (2)

Largest point moved by a permutation:

PermutationMax[Cycles[{{1,6,3},{2,5,12,9}}]]

Largest point moved in a permutation list:

PermutationMax[{1,4,3,10,2,6,5,7,9,8,11}]

OpenersExampleSection1(Spacer1)Scope  (2)

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

PermutationMax[Cycles[{{1,5,3,7},{2,6,10,8,4}}]]

Maximum of the support of the identity:

PermutationMax[Cycles[{}]]

Largest integer of the support of a permutation list:

PermutationMax[{7,4,5,8,1,2,3,10,9,6,11,12,13}]

Maximum of the support of the identity permutation list:

PermutationMax[{1,2,3,4,5}]

OpenersExampleSection2(Spacer1)Generalizations & Extensions  (1)

Largest integer moved by the elements of a permutation group:

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

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

PermutationLength[DihedralGroup[5]]

OpenersExampleSection4(Spacer1)Properties & Relations  (2)

On (RefLink[Cycles, paclet:ref/Cycles]) objects, (RefLink[PermutationMax, paclet:ref/PermutationMax]) is equivalent to applying (RefLink[Max, paclet:ref/Max]):

PermutationMax[Cycles[{{1,6,3},{2,5,12,9}}]]===Max@@Cycles[{{1,6,3},{2,5,12,9}}]

On both (RefLink[Cycles, paclet:ref/Cycles]) objects and permutation lists, (RefLink[PermutationMax, paclet:ref/PermutationMax]) is equivalent to applying (RefLink[Max, paclet:ref/Max]) on the permutation support:

PermutationMax[{1,4,3,10,2,6,5,7,9,8,11}]===Max@PermutationSupport[{1,4,3,10,2,6,5,7,9,8,11}]

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