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Mathematica > Mathematics and Algorithms > Discrete Mathematics > Permutations > PermutationPower >

BUILT-IN MATHEMATICA SYMBOL

PermutationPower

gives the n

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:

Out[1]=

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: