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based on an earlier version of the Wolfram Language.
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PermutationPower

PermutationPower
gives the n^(th) permutation power of the permutation perm.
  • PermutationPower effectively computes the product of a permutation perm with itself n times.
  • When n is negative, PermutationPower finds powers of the inverse of the permutation perm.
Sixth power of a permutation:
Second power of the inverse permutation:
PermutationPower can yield the identity permutation:
Sixth power of a permutation:
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Second power of the inverse permutation:
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PermutationPower can yield the identity permutation:
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Compute arbitrary powers of a permutation:
PermutationPower does not evaluate for symbolic arguments:
PermutationPower performs some simplifications for generic symbolic input:
For exponents that are multiples of the order of the permutation, the permutation power yields identity:
Hence large powers can be reduced by using the modulo of the exponent:
New in 8