Séminaire Lotharingien de Combinatoire, B85b (2021), 5 pp.

Miklós Bóna

Generating Functions of Permutations with Respect to Their Alternating Runs

Abstract. We present a short, direct proof of the fact that the generating function of all permutations of a fixed length n ≥ 4 with respect to the number of their alternating runs is divisible by (1+z)m, where m = ⌊(n-2)/2⌋.


Received: March 29, 2021. Revised: May 19, 2021. Accepted: May 19, 2021.

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