Thin polytopes: lattice polytopes with vanishing local \(h^*\)-polynomial
type: Item
instance of: scholarly article
title: Thin polytopes: lattice polytopes with vanishing local \(h^*\)-polynomial
author: Christopher Borger
author: Andreas Kretschmer
author: Benjamin Nill
published in: IMRN. International Mathematics Research Notices
publication date: 2024-10-24T00:00:00Z
review text: A lattice polytope is \textit{thin} if its local \(h^*\)-polynomials vanish. The study of thin simplices was originated by Gelfand, Kapranov, and Zelevinsky; for simplices the local \(h^*\)-polynomial equals the box polynomial.\N\NThe paper starts with a survey of existing results around \(h\)- and \(g\)-polynomials and Ehrhart theory.\N\NThe main results are the complete classification of thin polytopes up to dimension \(3\) and the characterization of thinness for Gorenstein polytopes.
Mathematics Subject Classification ID: 52B20
zbMATH DE Number: 7931171
zbMATH Keywords: Ehrhart theory
zbMATH Keywords: \(g\)-polynomial
zbMATH Keywords: \(h\)-polynomial
zbMATH Keywords: lattice polytopes
zbMATH Keywords: Gorenstein polytopes
MaRDI profile type: Publication
DOI: 10.1093/IMRN/RNAD231
description: scientific article; zbMATH DE number 7931171