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Ehrhart polynomial roots of reflexive polytopes

KASPRZYK, ALEXANDER; Hegedus, Gabor; Higashitani, Akihiro

Authors

ALEXANDER KASPRZYK

Gabor Hegedus

Akihiro Higashitani



Abstract

Recent work has focused on the roots z∈C of the Ehrhart polynomial of a lattice polytope P. The case when Rz=−1/2 is of particular interest: these polytopes satisfy Golyshev's "canonical line hypothesis". We characterise such polytopes when dim(P)≤7. We also consider the "half-strip condition", where all roots z satisfy −dim(P)/2≤Rz≤dim(P)/2−1, and show that this holds for any reflexive polytope with dim(P)≤5. We give an example of a 10-dimensional reflexive polytope which violates the half-strip condition, thus improving on an example by Ohsugi–Shibata in dimension 34.

Journal Article Type Article
Publication Date Mar 8, 2019
Electronic ISSN 1077-8926
Publisher Electronic Journal of Combinatorics
Peer Reviewed Peer Reviewed
Volume 26
Issue 1
Article Number P1.38
APA6 Citation KASPRZYK, A., Hegedus, G., & Higashitani, A. (2019). Ehrhart polynomial roots of reflexive polytopes. Electronic Journal of Combinatorics, 26(1),
Publisher URL https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i1p38

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