On the roots of the Poupard and Kreweras polynomials
Combinatorics
2020-01-07 v1
Abstract
The Poupard polynomials are polynomials in one variable with integer coefficients, with some close relationship to Bernoulli and tangent numbers. They also have a combinatorial interpretation. We prove that every Poupard polynomial has all its roots on the unit circle. We also obtain the same property for another sequence of polynomials introduced by Kreweras and related to Genocchi numbers. This is obtained through a general statement about some linear operators acting on palindromic polynomials.
Keywords
Cite
@article{arxiv.2001.01449,
title = {On the roots of the Poupard and Kreweras polynomials},
author = {Frédéric Chapoton and Guo-Niu Han},
journal= {arXiv preprint arXiv:2001.01449},
year = {2020}
}
Comments
10 pages, 1 figure