Oriented matroids with few mutations

DOI10.1007/BF02573980zbMath0789.05022MaRDI QIDQ688011

Jürgen Richter-Gebert

Publication date: 12 June 1994

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

zbMATH Keywords

hyperplaneoriented matroidspseudoarrangementspseudoplane arrangementssimplicial regions

Mathematics Subject Classification ID

Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Combinatorial aspects of matroids and geometric lattices (05B35)

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Cites Work

• Unnamed Item
• Combinatorial models for the finite-dimensional Grassmannians
• Two constructions of oriented matroids with disconnected extension space
• Simplicial cells in arrangements and mutations of oriented matroids
• Simplicial cells in arrangements of hyperplanes
• Convexity in oriented matroids
• Three points do not determine a (pseudo-) plane
• Computational synthetic geometry
• Oriented matroids
• A lower bound on the number of cells in arrangements of hyperplanes
• Orientability of matroids
• A combinatorial abstraction of linear programming
• Extension spaces of oriented matroids