, Volume 5, Issue 1, pp 23-32

Combinatorial representation and convex dimension of convex geometries

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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.

Communicated by D. Kelly
Supported in part by NSF grant no. DMS-8501948.