Interlacing Ehrhart Polynomials of Reflexive Polytopes
Combinatorics
2018-04-20 v1
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.
Cite
@article{arxiv.1612.07538,
title = {Interlacing Ehrhart Polynomials of Reflexive Polytopes},
author = {Akihiro Higashitani and Mario Kummer and Mateusz Michałek},
journal= {arXiv preprint arXiv:1612.07538},
year = {2018}
}