Abstract
We prove that convex geometries of convex dimension n that satisfy two properties satisfied by nondegenerate sets of points in the plane, may have no more than 2 n-1 points. We give examples of such convex geometries that have n \choose 4 + n \choose 2 + n \choose 0 points.
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Received June 7, 1999, and in revised form April 18, 2000. Online publication September 22, 2000.
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Morris, W. Convex Dimension of Locally Planar Convex Geometries. Discrete Comput Geom 25, 85–101 (2001). https://doi.org/10.1007/s004540010073
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DOI: https://doi.org/10.1007/s004540010073