On the Order Dimension of Convex Geometries

Details On the Order Dimension of Convex Geometries On the Order Dimension of Convex Geometries

2011-09-12

arxiv.org/abs/1109.2561v1

Mathematics

Combinatorics

12 pages, 2 figures

Scientific paper

We study the order dimension of the lattice of closed sets for a convex geometry. Further, we prove the existence of large convex geometries realized by planar point sets that have very low order dimension. We show that the planar point set of Erdos and Szekeres from 1961 which is a set of 2^(n-2) points and contains no convex n-gon has order dimension n - 1 and any larger set of points has order dimension strictly larger than n - 1.

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