Do alcoved lattice polytopes have unimodal h*-vector?
Combinatorics
2021-05-03 v1
Abstract
We show that h*-vectors of alcoved polytopes P in R^n (of Lie type A) are unimodal if they contain interior lattice points and their facets have lattice distance 1 to the set of interior lattice points. The maximal possible such distance for general alcoved polytopes is shown to be dim(P)-1. A secondary purpose of the paper is to serve as a guide to previous work surrounding unimodality of h*-vectors of alcoved polytopes and related questions.
Keywords
Cite
@article{arxiv.2104.15080,
title = {Do alcoved lattice polytopes have unimodal h*-vector?},
author = {Rainer Sinn and Hannah Sjöberg},
journal= {arXiv preprint arXiv:2104.15080},
year = {2021}
}