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Permutation from SubexcedantSeq ​

The permutation a subexcedant sequence is the inversion sequence of.

SubexcedantSeq → Permutationinverse

Declines a word that isn't subexcedant: entry i must lie in 0..i − 1.

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: CycleDecomposition.