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Interlacing Ehrhart Polynomials of Reflexive Polytopes

By Akihiro Higashitani, Mario Kummer and Mateusz Michałek

Abstract

It was observed by Bump et al. that Ehrhart polynomials in a special family exhibit properties similar to the Riemann {\zeta} function. The construction was generalized by Matsui et al. to a larger family of reflexive polytopes coming from graphs. We prove several conjectures confirming when such polynomials have zeros on a certain line in the complex plane. Our main new method is to prove a stronger property called interlacing

Topics: Mathematics - Combinatorics
Publisher: 'Springer Science and Business Media LLC'
Year: 2016
DOI identifier: 10.1007/s00029-017-0350-6
OAI identifier: oai:arXiv.org:1612.07538

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