NBC Complexes of Convex Geometries - Kenji Kashiwabara; Masataka Nakamura (Discrete Mathematics & Theoretical Computer Science, 2005)
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.