Embedding convex geometries and a bound on convex dimension

by Michael Richter, Luke G. Rogers

The notion of an abstract convex geometry offers an abstraction of the standard notion of convexity in a linear space. Kashiwabara, Nakamura and Okamoto introduce the notion of a generalized convex shelling into R and prove that a convex geometry may always be represented with such a shelling. We provide a new, shorter proof of their result using a recent representation theorem of Richter and Rubinstein, and deduce a different upper bound on the dimension of the shelling.

Arxiv preprint version

Published version in Discrete Math