Ehrhart series, unimodality, and integrally closed reflexive polytopes
Combinatorics
2014-08-28 v3
Abstract
An interesting open problem in Ehrhart theory is to classify those lattice polytopes having a unimodal -vector. Although various sufficient conditions have been found, necessary conditions remain a challenge. In this paper, we consider integrally closed reflexive simplices and discuss an operation that preserves reflexivity, integral closure, and unimodality of the -vector, providing one explanation for why unimodality occurs in this setting. We also discuss the failure of proving unimodality in this setting using weak Lefschetz elements.
Keywords
Cite
@article{arxiv.1403.5378,
title = {Ehrhart series, unimodality, and integrally closed reflexive polytopes},
author = {Benjamin Braun and Robert Davis},
journal= {arXiv preprint arXiv:1403.5378},
year = {2014}
}