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.
| Original language | English |
|---|---|
| Pages (from-to) | 705-717 |
| Number of pages | 13 |
| Journal | Annals of Combinatorics |
| Volume | 20 |
| Issue number | 4 |
| DOIs | |
| State | Published - Dec 1 2016 |
Bibliographical note
Publisher Copyright:© 2016, Springer International Publishing.
Keywords
- Ehrhart series
- reflexive polytopes
- unimodal sequence
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
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