KrewerasComplement
w⁻¹c, for w below the long cycle c = (1 2 ... n) in absolute order.
KrewerasComplement(Permutation)
Details
- Takes a `Permutation` and returns a `Permutation` — a typed map, so a wrong carrier is a type error rather than a wrong answer.
- Only defined on the non-crossing permutations (the embedding of NC(n) in S_n by absolute order beneath c) — everywhere else this declines rather than answering for a word it was never defined on. K∘K is conjugation by c, and K is a bijection of NC(n) onto itself.