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arXiv · 1403.5378

Ehrhart series, unimodality, and integrally closed reflexive polytopes

Benjamin Braun·Robert Davis
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Abstract

An interesting open problem in Ehrhart theory is to classify those lattice polytopes having a unimodal $h^*$-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 $h^*$-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.

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Benjamin Braun, Robert Davis. 2014-08-27. Ehrhart series, unimodality, and integrally closed reflexive polytopes. https://arxiv.org/abs/1403.5378

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