 Alternating-permutation convolution

ID: alternating-permutation-convolution

Codex  0 Created 2026-09-24 Updated 2026-09-24

Splitting an alternating permutation at its maximum gives

2 A_{n + 1} = \sum_{k = 0}^{n} (k n) A_{k} A_{n - k},

where

A_{n}

counts up-down permutations and complementation identifies up-down with down-up permutations.

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