A characterization of oriented matroids in terms of topes

DOI10.1016/S0195-6698(13)80054-6zbMath0748.05042MaRDI QIDQ1813626

Keiichi Handa

Publication date: 25 June 1992

Published in: European Journal of Combinatorics (Search for Journal in Brave)

zbMATH Keywords

oriented matroidacyclic setscocircuit spantope

Mathematics Subject Classification ID

Combinatorial aspects of matroids and geometric lattices (05B35)

Related Items

Topes of oriented matroids and related structures ⋮ Vapnik-Chervonenkis dimension and (pseudo-)hyperplane arrangements ⋮ Axioms for maximal vectors of an oriented matroid: A combinatorial characterization of the regions determined by an arrangement of pseudohyperplanes ⋮ An axiomatic of non-Radon partitions of oriented matroids ⋮ When Can Splits be Drawn in the Plane? ⋮ Corners and simpliciality in oriented matroids and partial cubes ⋮ On \(k\)-neighborly reorientations of oriented matroids ⋮ Symmetry, oriented matroids and two conjectures of Michel Las Vergnas ⋮ A homotopy theorem on oriented matroids ⋮ On fillings of \(2N\)-gons with rhombi ⋮ Antipodal graphs and oriented matroids ⋮ On tope graphs of complexes of oriented matroids ⋮ Mirror graphs: graph theoretical characterization of reflection arrangements and finite Coxeter groups

Cites Work

• The acyclic sets of an oriented matroid
• A combinatorial perspective on the non-Radon partitions
• A problem of McMullen on the projective equivalences of polytopes
• An axiomatic of non-Radon partitions of oriented matroids
• Convexity in oriented matroids
• Lopsided sets and orthant-intersection by convex sets
• Sur les matroides orientes de rang 3 et les arrangements de pseudodroites dans le plan projectif réel
• Oriented matroids
• Orientability of matroids