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2020 On the roots of the Poupard and Kreweras polynomials
Frédéric Chapoton, Guo-Niu Han
Mosc. J. Comb. Number Theory 9(2): 163-172 (2020). DOI: 10.2140/moscow.2020.9.163

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.

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Frédéric Chapoton. Guo-Niu Han. "On the roots of the Poupard and Kreweras polynomials." Mosc. J. Comb. Number Theory 9 (2) 163 - 172, 2020. https://doi.org/10.2140/moscow.2020.9.163

Information

Received: 16 January 2020; Revised: 15 May 2020; Accepted: 29 May 2020; Published: 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07248533
MathSciNet: MR4131794
Digital Object Identifier: 10.2140/moscow.2020.9.163

Subjects:
Primary: 26C10, 47B39
Secondary: 11B68, 39A70

Rights: Copyright © 2020 Mathematical Sciences Publishers

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