Regular Unimodular Triangulations of Reflexive IDP 2-Supported Weighted Projective Space Simplices

Benjamin Braun, Derek Hanely

Research output: Contribution to journalArticlepeer-review

Abstract

For each integer partition q with d parts, we denote by Δ (1,q) the lattice simplex obtained as the convex hull in Rd of the standard basis vectors along with the vector - q. For q with two distinct parts such that Δ (1,q) is reflexive and has the integer decomposition property, we establish a characterization of the lattice points contained in Δ (1,q). We then construct a Gröbner basis with a squarefree initial ideal of the toric ideal defined by these simplices. This establishes the existence of a regular unimodular triangulation for reflexive 2-supported Δ (1,q) having the integer decomposition property. As a corollary, we obtain a new proof that these simplices have unimodal Ehrhart h-vectors.

Original languageEnglish
Pages (from-to)935-960
Number of pages26
JournalAnnals of Combinatorics
Volume25
Issue number4
DOIs
StatePublished - Dec 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Fingerprint

Dive into the research topics of 'Regular Unimodular Triangulations of Reflexive IDP 2-Supported Weighted Projective Space Simplices'. Together they form a unique fingerprint.

Cite this