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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