Some coefficient sequences related to the descent polynomial
Ferenc Bencs

TL;DR
This paper investigates the coefficient sequences of descent polynomials, proving conjectures and identifying zero-free regions, thereby advancing understanding of permutation descent structures.
Contribution
It proves conjectures related to descent polynomial coefficients and describes zero-free regions, offering new insights into permutation descent polynomials.
Findings
Proved conjectures on coefficient sequences
Identified zero-free regions for descent polynomials
Enhanced understanding of descent polynomial properties
Abstract
The descent polynomial of a finite is the polynomial , for which the evaluation at is the number of permutations on elements, such that is the set of indices where the permutation is descending. In this paper we will prove some conjectures concerning coefficient sequences of . As a corollary we will describe some zero-free regions for the descent polynomial.
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