Some identities involving derangement polynomials and numbers
Number Theory
2020-11-04 v1
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.
Keywords
Cite
@article{arxiv.2011.01577,
title = {Some identities involving derangement polynomials and numbers},
author = {Taekyun Kim and Dae San Kim and Lee-Chae Jang and Hyunseok Lee},
journal= {arXiv preprint arXiv:2011.01577},
year = {2020}
}
Comments
13 pages