2021/04/30 by Rainer Sinn, Sinn, Rainer, Hannah Sjöberg +1
Computer Science · Engineering · Mathematics · #Advanced Combinatorial Mathematics #Computational Geometry and Mesh Generation #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.2104.15080
arxiv created 2021/04/30 · arxiv updated 2021/05/03
We show that h*-vectors of alcoved polytopes P in Rn (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.