Kenji Kashiwabara ; Masataka Nakamura - NBC Complexes of Convex Geometries

dmtcs:3412 - Discrete Mathematics & Theoretical Computer Science, January 1, 2005, DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05) - https://doi.org/10.46298/dmtcs.3412
NBC Complexes of Convex GeometriesArticle

Authors: Kenji Kashiwabara 1; Masataka Nakamura 1

  • 1 Department of Quantum Engineering and Systems Science, Graduate School of Engineering The University of Tokyo

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.

https://doi.org/10.46298/dmtcs.3412
Source: HAL:hal-01184369v1
Volume: DMTCS Proceedings vol. AE, European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Section: Proceedings
Published on: January 1, 2005
Imported on: May 10, 2017
Keywords: broken circuit,characteristic polynomial,NBC basis theorem,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM],[MATH.MATH-CO] Mathematics [math]/Combinatorics [math.CO]

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