## 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)

### Stefan Felsner (ed.)

### DMTCS Conference Volume AE (2005), pp. 207-212

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]. |

If your browser does not display the abstract correctly (because of the different mathematical symbols) you may look it up in the PostScript or PDF files. | |

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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Automatically produced on Di Sep 27 10:09:53 CEST 2005 by gustedt