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Unconditional reflexive polytopes

  • A 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.

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Author:Florian KohlORCiDGND, McCabe Olsen, Raman SanyalORCiDGND
URN:urn:nbn:de:hebis:30:3-813072
DOI:https://doi.org/10.1007/s00454-020-00199-8
ISSN:1432-0444
Parent Title (English):Discrete & computational geometry
Publisher:Springer
Place of publication:New York, NY ; [Berlin ; Heidelberg]
Document Type:Article
Language:English
Date of Publication (online):2020/04/16
Date of first Publication:2020/04/16
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2024/02/28
Tag:Gale-dual pairs; Perfect graphs; Reflexive polytopes; Signed Birkhoff polytopes; Unconditional polytopes; Unimodular triangulations
Volume:64
Issue:2
Page Number:26
First Page:427
Last Page:452
Note:
Open Access funding provided by Projekt DEAL.
Institutes:Informatik und Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:05-XX COMBINATORICS (For finite fields, see 11Txx) / 05Cxx Graph theory (For applications of graphs, see 68R10, 81Q30, 81T15, 82B20, 82C20, 90C35, 92E10, 94C15) / 05C17 Perfect graphs
52-XX CONVEX AND DISCRETE GEOMETRY / 52Bxx Polytopes and polyhedra / 52B12 Special polytopes (linear programming, centrally symmetric, etc.)
52-XX CONVEX AND DISCRETE GEOMETRY / 52Bxx Polytopes and polyhedra / 52B15 Symmetry properties of polytopes
52-XX CONVEX AND DISCRETE GEOMETRY / 52Bxx Polytopes and polyhedra / 52B20 Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International

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