Geodesic
NBC Complexes of Convex Geometries
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005).

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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. 
@article{DMTCS_2005_special_250_a21,
     author = {Kashiwabara, Kenji and Nakamura, Masataka},
     title = {NBC {Complexes} of {Convex} {Geometries}},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)},
     year = {2005},
     doi = {10.46298/dmtcs.3412},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3412/}
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Kashiwabara, Kenji; Nakamura, Masataka. NBC Complexes of Convex Geometries. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) (2005). doi : 10.46298/dmtcs.3412. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.3412/

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