| author: | Kenji Kashiwabara and Masataka Nakamura |
|---|---|
| title: | NBC Complexes of Convex Geometries |
| keywords: | broken circuit, characteristic polynomial, NBC basis theorem |
| abstract: | 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. This note is on the same line as the studies in [nakamura03a, okamoto-nakamura, nakamura]. |
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| reference: | Kenji Kashiwabara and Masataka Nakamura (2005), NBC Complexes of Convex Geometries, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 207-212 |
| bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |
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