Séminaire Lotharingien de Combinatoire, 86B.81 (2022), 10 pp.
Andrew O'Desky and David Harry Richman
Derangements and the p-Adic Incomplete Gamma Function
Abstract.
The derangement-counting sequence satisfies strong p-adic regularity properties.
We prove that these p-adic properties generalize to various other derangement-like sequences.
To fit these observations into a unified framework, we show the existence of a p-adic analogue of the incomplete gamma function.
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
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