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On the roots of the
Poupard and Kreweras polynomials
Frédéric Chapoton and Guo-Niu Han |
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Vol. 9 (2020), No. 2, 163–172
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DOI: 10.2140/moscow.2020.9.163
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Abstract |
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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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Keywords
palindromic polynomial, unit circle, complex root, linear
operator, Bernoulli number
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Mathematical Subject Classification 2010
Primary: 26C10, 47B39
Secondary: 11B68, 39A70
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Milestones
Received: 16 January 2020
Revised: 15 May 2020
Accepted: 29 May 2020
Published: 7 August 2020
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Authors |
| Frédéric Chapoton | |
| Institut de Recherche Mathématique
Avancée UMR 7501 Université de Strasbourg et CNRS Strasbourg France |
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| Guo-Niu Han | |
| Institut de Recherche Mathématique
Avancée UMR 7501 Université de Strasbourg et CNRS Strasbourg France |
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