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KrewerasComplement

w⁻¹c, for w below the long cycle c = (1 2 ... n) in absolute order.

KrewerasComplement(Permutation)

Domain: Combinatorial maps

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.

Examples