ALEXANDER KASPRZYK A.M.KASPRZYK@NOTTINGHAM.AC.UK
Associate Professor
Ehrhart polynomial roots of reflexive polytopes
KASPRZYK, ALEXANDER; Hegedus, Gabor; Higashitani, Akihiro
Authors
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.
Citation
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 | https://nottingham-repository.worktribe.com/output/1605870 |
Publisher URL | https://www.combinatorics.org/ojs/index.php/eljc/article/view/v26i1p38 |
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Publisher Licence URL
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