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Permutation from CycleDecomposition ​

The permutation a cycle decomposition describes.

CycleDecomposition → Permutationinverse

Declines a decomposition that isn't canonical: a point missing or repeated, a cycle not starting at its least point, or cycles out of order.

Called as CombinatorialMap(x, "Permutation"). The head's page has its examples.

Also from

The same name out of other carriers, each its own implementation: SubexcedantSeq.