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NBC Complexes of Convex Geometries

Abstract : We introduce a notion of a $\textit{broken circuit}$ and an $\textit{NBC complex}$ 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.
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Kenji Kashiwabara, Masataka Nakamura. NBC Complexes of Convex Geometries. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. pp.207-212, ⟨10.46298/dmtcs.3412⟩. ⟨hal-01184369⟩

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