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MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
7/2017

Interlacing Ehrhart Polynomials of Reflexive Polytopes

Akihiro Higashitani, Mario Denis 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.

Received:
Jan 9, 2017
Published:
Jan 30, 2017
MSC Codes:
26C10

Related publications

inJournal
2017 Journal Open Access
Akihiro Higashitani, Mario Kummer and Mateusz Michałek

Interlacing Ehrhart polynomials of reflexive polytopes

In: Selecta mathematica, 23 (2017) 4, pp. 2977-2998