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arXiv · 2011.01577

Some identities involving derangement polynomials and numbers

Taekyun Kim·Dae San Kim·Lee-Chae Jang·Hyunseok Lee
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Abstract

The problem of counting derangements was initiated by Pierre Remonde de Motmort in 1708. A derangement is a permutation that has no fixed points and the derangement number Dn is the number of fixed point free permutations on an n element set. Furthermore, the derangement polynomials are natural extensions of the derangement numbers. In this paper, we study the derangement polynomials and numbers, their connections with cosine-derangement polynomials and sine-derangement polynomials and their applications to moments of some variants of gamma random variables.

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Taekyun Kim, Dae San Kim, Lee-Chae Jang, Hyunseok Lee. 2020-11-03. Some identities involving derangement polynomials and numbers. https://arxiv.org/abs/2011.01577

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