Ehrhart polynomial roots of reflexive polytopes

KASPRZYK, ALEXANDER; Hegedus, Gabor; Higashitani, Akihiro

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.

Citation

KASPRZYK, A., Hegedus, G., & Higashitani, A. (2019). Ehrhart polynomial roots of reflexive polytopes. Electronic Journal of Combinatorics, 26(1), Article P1.38

• Journal Article Type: Article
• Acceptance Date: Jan 2, 2019
• Online Publication Date: Mar 8, 2019
• Publication Date: Mar 8, 2019
• Deposit Date: Mar 14, 2019
• Publicly Available Date: Mar 15, 2019
• Electronic ISSN: 1077-8926
• Publisher: Electronic Journal of Combinatorics
• Peer Reviewed: Peer Reviewed
• Volume: 26
• Issue: 1
• Article Number: P1.38
• Keywords: Combinatorics; Algebraic Geometry
• Public URL: https://nottingham-repository.worktribe.com/output/1605870
• Publisher URL: https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i1p38
• Contract Date: Mar 14, 2019