A topological representation theorem for tropical oriented matroids

DOI10.1016/j.jcta.2016.03.003zbMath1337.05113OpenAlexW2055354724MaRDI QIDQ285065

Silke Horn

Publication date: 18 May 2016

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2016.03.003

zbMATH Keywords

oriented matroidstropical geometrymixed subdivisionstopological representation theoremtropical hyperplanestropical oriented matroidstropical pseudohyperplanes

Mathematics Subject Classification ID

Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40)

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Cites Work

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• A topological representation theorem for tropical oriented matroids
• Triangulations. Structures for algorithms and applications
• Oriented matroids
• The Cayley trick, lifting subdivisions and the Bohne-Dress theorem on zonotopal tilings
• Tropical convexity
• Flag arrangements and triangulations of products of simplices
• Tropical hyperplane arrangements and oriented matroids
• Non-connected toric Hilbert schemes
• The Bergman complex of a matroid and phylogenetic trees
• Triangulations of $\Delta_{n-1} \times \Delta_{d-1}$ and Tropical Oriented Matroids
• Oriented Matroids
• A Topological Representation Theorem for Tropical Oriented Matroids: Part I
• Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes