Algebraic varieties characterizing matroids and oriented matroids

DOI10.1016/0001-8708(91)90070-NzbMath0762.05030OpenAlexW1967481256MaRDI QIDQ1175763

Jürgen Bokowski, Jürgen Richter-Gebert, António Guedes de Oliveira

Publication date: 25 June 1992

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(91)90070-n

zbMATH Keywords

matroidsoriented matroidsalgebraic varietiesGrassmann varietychirotope varietycomputational synthetic geometrymatroid variety

Mathematics Subject Classification ID

Combinatorial aspects of matroids and geometric lattices (05B35)

Related Items

On the Steinitz exchange lemma, A note on Gröbner bases, Weak orientability of matroids and polynomial equations

Uses Software

• AS 127

Cites Work

• Nonrealizability proofs in computational geometry
• Convexity in oriented matroids
• Proof of Grünbaum's conjecture on the stretchability of certain arrangements of pseudolines
• Sur les matroides orientes de rang 3 et les arrangements de pseudodroites dans le plan projectif réel
• A new Sylvester-Gallai configuration representing the 13-point projective plane in \(R^ 4\)
• Computational synthetic geometry
• Oriented matroids
• Orientability of matroids
• Bases in oriented matroids
• Grassmann-Plücker relations and matroids with coefficients
• On the coordinatization of oriented matroids
• Oriented matroids and multiply ordered sets
• Some properties of basic families of subsets
• On n-ordered sets and order completeness
• Algorithm AS 127: Generation of Random Orthogonal Matrices
• The Bracket Ring of a Combinatorial Geometry. I
• A Multiple Exchange Property for Bases
• Theory of Matroids
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