Unconditional Reflexive Polytopes
| Autor: | McCabe Olsen, Florian Kohl, Raman Sanyal |
|---|---|
| Přispěvatelé: | Department of Mathematics and Systems Analysis, Ohio State University, Goethe University Frankfurt, Aalto-yliopisto, Aalto University |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Perfect graphs
Polytope 0102 computer and information sciences Unconditional polytopes Unimodular triangulations Lattice (discrete subgroup) 01 natural sciences Prime (order theory) Theoretical Computer Science Combinatorics Reflexivity FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Mathematics::Metric Geometry 0101 mathematics Mathematics Mathematics::Functional Analysis Mathematics::Combinatorics Birkhoff polytope 010102 general mathematics Gale-dual pairs Computational Theory and Mathematics Hyperplane 010201 computation theory & mathematics Reflexive polytopes Signed Birkhoff polytopes Convex body Geometry and Topology Combinatorics (math.CO) Partially ordered set |
| Popis: | 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 Comment: 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 |
| Databáze: | OpenAIRE |
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