Some coefficient sequences related to the descent polynomial

Abstract

The descent polynomial of a finite I⊆Z+ is the polynomial d(I,n), for which the evaluation at n>max(I) is the number of permutations on n elements, such that I is the set of indices where the permutation is descending. In this paper, we will prove some conjectures concerning coefficient sequences of d(I,n). As a corollary, we will describe some zero-free regions for the descent polynomial.