vix.ing · top · new · best · stats · spec

On counterexamples to a conjecture of Wills and Ehrhart polynomials\n whose roots have equal real parts

2013/09/03 by Matthias Henze, Henze, Matthias
Computer Science · Mathematics · Medicine · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #Pharmacological Effects of Medicinal Plants #Point processes and geometric inequalities #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1309.0725

openalex publication_date 2013/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

As a discrete analog to Minkowski's theorem on convex bodies, Wills\nconjectured that the Ehrhart coefficients of a centrally symmetric lattice\npolytope with exactly one interior lattice point are maximized by those of the\ncube of side length two. We discuss several counterexamples to this conjecture\nand, on the positive side, we identify a family of lattice polytopes that\nfulfill the claimed inequalities. This family is related to the recently\nintroduced class of l-reflexive polytopes.\n

Citations

Related