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.

The following versions are available: