Ehrhart Series, Unimodality, and Integrally Closed Reflexive Polytopes

Benjamin Braun, Robert Davis

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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 languageEnglish
Pages (from-to)705-717
Number of pages13
JournalAnnals of Combinatorics
Issue number4
StatePublished - Dec 1 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer International Publishing.


  • Ehrhart series
  • reflexive polytopes
  • unimodal sequence

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Ehrhart Series, Unimodality, and Integrally Closed Reflexive Polytopes'. Together they form a unique fingerprint.

Cite this