# 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.
Keywords :
Document type :
Conference papers
Domain :

Cited literature [13 references]

https://hal.inria.fr/hal-01184369
Contributor : Coordination Episciences Iam Connect in order to contact the contributor
Submitted on : Friday, August 14, 2015 - 11:37:53 AM
Last modification on : Monday, May 17, 2021 - 12:00:04 PM
Long-term archiving on: : Sunday, November 15, 2015 - 11:02:22 AM

### File

dmAE0141.pdf
Publisher files allowed on an open archive

### Citation

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⟩

Record views