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Mathematica > Mathematics and Algorithms > Discrete Mathematics > Permutations > PermutationSupport >

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PermutationSupport

PermutationSupport[perm]
returns the support of the permutation perm.

The support of a permutation perm is the list of integers that are not fixed by perm.

PermutationSupport works with Cycles objects as well as with permutation lists. When applied to a permutation list, PermutationSupport returns the for which .

Points moved by a permutation in disjoint cyclic form:

Points moved in a permutation list:

Points moved by a permutation in disjoint cyclic form:

Out[1]=

Points moved in a permutation list:

Out[1]=

Support of permutations in disjoint cyclic form:

Support of permutation lists:

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

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

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