2020/11/03 by Kim, Taekyun, Kim, Dae San, Jang, Lee-Chae +1
#11B73 #11B83 #65C50 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2011.01577
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.