COMs: complexes of oriented matroids

DOI10.1016/j.jcta.2018.01.002zbMath1381.05008arXiv1507.06111OpenAlexW2962867705MaRDI QIDQ1703453

Victor Chepoi, Hans-Jürgen Bandelt, Kolja Knauer

Publication date: 2 March 2018

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

Full work available at URL: https://arxiv.org/abs/1507.06111

zbMATH Keywords

oriented matroidcell complexcocircuitlopsided setCoxeter zonotopetope graph

Mathematics Subject Classification ID

Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Combinatorial aspects of matroids and geometric lattices (05B35) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (19)

Unlabeled sample compression schemes and corner peelings for ample and maximum classes ⋮ Oriented matroids and combinatorial neural codes ⋮ The Varchenko matrix for topoplane arrangements ⋮ Ample Completions of Oriented Matroids and Complexes of Uniform Oriented Matroids ⋮ Cell complexes, poset topology and the representation theory of algebras arising in algebraic combinatorics and discrete geometry ⋮ The Varchenko determinant for apartments ⋮ Finitary affine oriented matroids ⋮ Corners and simpliciality in oriented matroids and partial cubes ⋮ First-order logic axiomatization of metric graph theory ⋮ Hyperplane Neural Codes and the Polar Complex ⋮ Distance-preserving subgraphs of Johnson graphs ⋮ The axiomatization of affine oriented matroids reassessed ⋮ Whitney numbers for poset cones ⋮ On tope graphs of complexes of oriented matroids ⋮ Hypercellular graphs: partial cubes without \(Q_3^-\) as partial cube minor ⋮ Two-dimensional partial cubes ⋮ The Varchenko determinant for oriented matroids ⋮ The Varchenko-Gel'fand ring of a cone ⋮ Mirror graphs: graph theoretical characterization of reflection arrangements and finite Coxeter groups

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• The bounded complex of a uniform affine oriented matroid is a ball
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• On the bounded complex of an affine oriented matroid
• A decomposition theorem for partially ordered sets
• Random Walks, Arrangements, Cell Complexes, Greedoids, and Self-Organizing Libraries
• The Graph of Linear Extensions Revisited
• Oriented Matroids
• Geometry of cuts and metrics

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