A circuit set characterization of antimatroids
Journal of Combinatorial Theory Series A
Matroids and antimatroids—a survey
Discrete Mathematics
An algorithmic characterization of antimatroids
Discrete Applied Mathematics
Monotone structure in discrete-event systems
Monotone structure in discrete-event systems
Knowledge Spaces
A greedy algorithm for convex geometries
Discrete Applied Mathematics - Submodularity
Matrices and Matroids for Systems Analysis
Matrices and Matroids for Systems Analysis
Dual greedy polyhedra, choice functions, and abstract convex geometries
Discrete Optimization
Realization of abstract convex geometries by point configurations
European Journal of Combinatorics
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A convex geometry is a combinatorial abstract model introduced by Edelman and Jamison which captures a combinatorial essence of "convexity" shared by some objects including finite point sets, partially ordered sets, trees, rooted graphs. In this paper, we introduce a generalized convex shelling, and show that every convex geometry can be represented as a generalized convex shelling. This is "the representation theorem for convex geometries" analogous to "the representation theorem for oriented matroids" by Folkman and Lawrence. An important feature is that our representation theorem is affine-geometric while that for oriented matroids is topological. Thus our representation theorem indicates the intrinsic simplicity of convex geometries, and opens a new research direction in the theory of convex geometries.