English

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

R2 v1 2026-06-23T19:52:46.886Z