NBC Complexes of Convex Geometries

Kenji Kashiwabara 1 Masataka Nakamura 1
1 Department of Quantum Engineering and Systems Science, Graduate School of Engineering The University of Tokyo
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.
Keywords : broken circuit characteristic polynomial NBC basis theorem
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Communication dans un congrès
Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.207-212, 2005, DMTCS Proceedings
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Kenji Kashiwabara, Masataka Nakamura. NBC Complexes of Convex Geometries. Stefan Felsner. 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), 2005, Berlin, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), pp.207-212, 2005, DMTCS Proceedings. 〈hal-01184369〉

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