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• W2952448168 abstract "Let F be a finite set of circles in the plane. We point out that the usual convex closure restricted to F yields a convex geometry, that is, a combinatorial structure introduced by P. H Edelman in 1980 under the name anti-exchange closure system. We prove that if the circles are collinear and they are arranged in a concave way, then they determine a convex geometry of convex dimension at most 2, and each finite convex geometry of convex dimension at most 2 can be represented this way. The proof uses some recent results from Lattice Theory, and some of the auxiliary statements on lattices or convex geometries could be of separate interest. The paper is concluded with some open problems." @default.
• W2952448168 created "2019-06-27" @default.
• W2952448168 creator A5070558748 @default.
• W2952448168 date "2012-12-14" @default.
• W2952448168 modified "2023-09-27" @default.
• W2952448168 title "Finite convex geometries of circles" @default.
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