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Ehrhart polynomial roots of reflexive polytopes

KASPRZYK, ALEXANDER; Hegedus, Gabor; Higashitani, Akihiro


Gabor Hegedus

Akihiro Higashitani


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.


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

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
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