DMTCS Proceedings, 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

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NBC Complexes of Convex Geometries

Kenji Kashiwabara, Masataka Nakamura


We introduce a notion of a broken circuit and an NBC complex for an (abstract) convex geometry. Based on these definitions, we shall show the analogues of the Whitney-Rota's formula and Brylawski's decomposition theorem for broken circuit complexes on matroids for convex geometries. We also present an Orlik-Solomon type algebra on a convex geometry, and show the NBC generating theorem. This note is on the same line as the studies in [nakamura03a, okamoto-nakamura, nakamura].

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