Some Identities on Derangement and Degenerate Derangement Polynomials

摘要

In combinatorics, a derangement is a permutation that has no fixed points.The number of derangements of an n-element set is called the n-th derangementnumber. In this paper, as natural companions to derangement numbers anddegenerate versions of the companions we introduce derangement polynomials anddegenerate derangement polynomials. We give some of their properties,recurrence relations and identities for those polynomials which are related tosome special numbers and polynomials.