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Combinatorial representation and convex dimension of convex geometries |
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| Authors: | Paul H. Edelman Michael E. Saks |
| Affiliation: | (1) Department of Mathematics, Carnegie-Mellon University, 15213 Pittsburgh, PA, USA;(2) Present address: Department of Mathematics, University of Minnesota, 55455 Minneapolis, MN, USA;(3) Department of Mathematics, Rutgers University, 08903 New Brunswick, NJ, USA;(4) Bell Communications Research, 07960 Morristown, NJ, USA |
| Abstract: | We develop a representation theory for convex geometries and meet distributive lattices in the spirit of Birkhoff's theorem characterizing distributive lattices. The results imply that every convex geometry on a set X has a canonical representation as a poset labelled by elements of X. These results are related to recent work of Korte and Lovász on antimatroids. We also compute the convex dimension of a convex geometry.Supported in part by NSF grant no. DMS-8501948. |
| Keywords: | 06A10 06B05 |
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