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

OpenersPrimaryExamplesSection(Spacer1)Examples  (7)

OpenersExampleSection0(Spacer1)Basic Examples  (2)

Smallest point moved by a permutation:

PermutationMin[Cycles[{{3,4,6},{2,7}}]]

Smallest point moved in a permutation list:

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

OpenersExampleSection1(Spacer1)Scope  (2)

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

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

Minimum of the support of the identity:

PermutationMin[Cycles[{}]]

Smallest integer of the support of a permutation list:

PermutationMin[{1,2,5,4,3,6,7}]

Minimum of the support of the identity permutation list:

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

OpenersExampleSection2(Spacer1)Generalizations & Extensions  (1)

Smallest integer moved by the elements of a permutation group:

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

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

PermutationMin[DihedralGroup[5]]

OpenersExampleSection4(Spacer1)Properties & Relations  (2)

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

PermutationMin[Cycles[{{3,4,6},{2,7}}]]===Min@@Cycles[{{3,4,6},{2,7}}]

On both (RefLink[Cycles, paclet:ref/Cycles]) objects and permutation lists, (RefLink[PermutationMin, paclet:ref/PermutationMin]) is equivalent to using (RefLink[Min, paclet:ref/Min]) on the permutation support:

PermutationMin[{1,2,5,4,3,6,7,8}]===Min@PermutationSupport[{1,2,5,4,3,6,7,8}]

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

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

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