Unconditional Reflexive Polytopes
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date
2020-09-01
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Language
en
Pages
26
427-452
427-452
Series
Discrete and Computational Geometry, Volume 64, issue 2
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.Description
Keywords
Gale-dual pairs, Perfect graphs, Reflexive polytopes, Signed Birkhoff polytopes, Unconditional polytopes, Unimodular triangulations
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Citation
Kohl, F, Olsen, M C & Sanyal, R 2020, ' Unconditional Reflexive Polytopes ', Discrete and Computational Geometry, vol. 64, no. 2, pp. 427-452 . https://doi.org/10.1007/s00454-020-00199-8