Taekyun Kim, Dae San Kim, Lee-Chae Jang, Hyunseok Lee
Published 2020-11-03Version 1
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.
Some identities and properties on degenerate Stirling numbers
Some identities on r-central factorial numbers and r-central Bell polynomials
Some identities involving degenerate r-Stirling numbers
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