Author:
Kohl Florian,Olsen McCabe,Sanyal Raman
Abstract
AbstractA convex body is unconditional if it is symmetric with respect to reflections in all coordinate hyperplanes. 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 Gröbner bases for unconditional reflexive polytopes coming from partially ordered sets.
Funder
Deutsche Forschungsgemeinschaft
Academy of Finland
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Theoretical Computer Science
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