Unconditional reflexive polytopes
Abstract
A convex body is unconditional if it is symmetric with respect to reflections in all coordinate hyperplanes. In this paper, we investigate unconditional lattice polytopes with respect to geometric, combinatorial, and algebraic properties. In particular, we characterize unconditional reflexive polytopes in terms of perfect graphs. As a prime example, we study the signed Birkhoff polytope. Moreover, we derive constructions for Gale-dual pairs of polytopes and we explicitly describe Gr\"obner bases for unconditional reflexive polytopes coming from partially ordered sets
Keywords
Cite
@article{arxiv.1906.01469,
title = {Unconditional reflexive polytopes},
author = {Florian Kohl and McCabe Olsen and Raman Sanyal},
journal= {arXiv preprint arXiv:1906.01469},
year = {2020}
}
Comments
20 pages, 5 tables, 2 figures; This paper supersedes arXiv:1903.12634; final version: To appear in Discrete and Computational Geometry, special issue in honor of Branko Grunbaum