Ehrhart Series, Unimodality, and Integrally Closed Reflexive Polytopes

Benjamin Braun; Robert Davis

doi:10.1007/s00026-016-0337-6

Ehrhart Series, Unimodality, and Integrally Closed Reflexive Polytopes

Benjamin Braun, Robert Davis

Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

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	https://doi.org/10.1007/s00026-016-0337-6
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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10.1007/s00026-016-0337-6

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AU - Davis, Robert

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AB - 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.

KW - Ehrhart series

KW - reflexive polytopes

KW - unimodal sequence

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Ehrhart Series, Unimodality, and Integrally Closed Reflexive Polytopes

Abstract

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Keywords

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