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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 |
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Pages (from-to) | 427-452 |
Number of pages | 26 |
Journal | Discrete and Computational Geometry |
Volume | 64 |
Issue number | 2 |
DOIs | |
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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- 1 Finished
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Algebraic structures and random geometry of stochastic lattice models
Kytölä, K., Gutiérrez, A. W., Kohl, F., Abuzaid, O., Webb, C., Karrila, A., Flores, S., Orlich, M. & Radnell, D.
01/09/2015 → 31/08/2019
Project: Academy of Finland: Other research funding