A circuit set characterization of antimatroids

DOI10.1016/0095-8956(87)90007-4zbMath0659.05036OpenAlexW2047348140MaRDI QIDQ1112050

Brenda L. Dietrich

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0095-8956(87)90007-4

zbMATH Keywords

convexitylinear dependenceAntimatroidscircuit elimination propertyRooted circuits

Mathematics Subject Classification ID

Combinatorial aspects of matroids and geometric lattices (05B35)

Related Items (21)

Convex geometries are extremal for the generalized Sauer-Shelah bound ⋮ \(n\)-distributivity, dimension and Carathéodory's theorem ⋮ On the topology of the free complexes of convex geometries ⋮ Optimum basis of finite convex geometry ⋮ A representation of antimatroids by Horn rules and its application to educational systems ⋮ What convex geometries tell about shattering-extremal systems ⋮ Matroids on convex geometries (cg-matroids) ⋮ Compressed representation of learning spaces ⋮ On scattered convex geometries ⋮ Representing finite convex geometries by relatively convex sets ⋮ Antimatroids, Betweenness, Convexity ⋮ A Sauer-Shelah-Perles lemma for lattices ⋮ Monge sequences, antimatroids, and the transportation problem with forbidden arcs ⋮ On the shelling antimatroids of split graphs ⋮ A unified interpretation of several combinatorial dualities ⋮ Mathematics of Plott choice functions ⋮ The affine representation theorem for abstract convex geometries ⋮ Characterizations of the convex geometries arising from the double shellings of posets ⋮ Translating between the representations of a ranked convex geometry ⋮ An abstract duality ⋮ Realization of abstract convex geometries by point configurations

Cites Work

• Structural properties of greedoids
• The theory of convex geometries
• Meet-distributive lattices and the anti-exchange closure
• Orientability of matroids
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