Unconditional Reflexive Polytopes

Florian Kohl; McCabe C. Olsen; Raman Sanyal

doi:10.1007/s00454-020-00199-8

Unconditional Reflexive Polytopes

Florian Kohl, McCabe C. Olsen, Raman Sanyal^*

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

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Abstract

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.

Original language	English
Pages (from-to)	427-452
Number of pages	26
Journal	Discrete and Computational Geometry
Volume	64
Issue number	2
DOIs	https://doi.org/10.1007/s00454-020-00199-8
Publication status	Published - 1 Sep 2020
MoE publication type	A1 Journal article-refereed

Keywords

Gale-dual pairs
Perfect graphs
Reflexive polytopes
Signed Birkhoff polytopes
Unconditional polytopes
Unimodular triangulations

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10.1007/s00454-020-00199-8

Kohl2020_Article_UnconditionalReflexivePolytopeFinal published version, 393 KBLicence: CC BY

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AU - Sanyal, Raman

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N2 - 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.

AB - 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.

KW - Gale-dual pairs

KW - Perfect graphs

KW - Reflexive polytopes

KW - Signed Birkhoff polytopes

KW - Unconditional polytopes

KW - Unimodular triangulations

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JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

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IS - 2

ER -

Unconditional Reflexive Polytopes

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Algebraic structures and random geometry of stochastic lattice models

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Unconditional Reflexive Polytopes

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Algebraic structures and random geometry of stochastic lattice models

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