PORTUGALIAEMATHEMATICA
Vol. 63, No. 3, pp. 363-374 (2006)
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PORTUGALIAE MATHEMATICA Vol. 63, No. 3, pp. 363-374 (2006) |
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An Orlik--Solomon type algebra for matroids with a fixed linear class of circuitsRaul Cordovil and David ForgeDepartamento de Matemática, Instituto Superior Técnico,Av. Rovisco Pais, 1049-001 Lisboa -- PORTUGAL E-mail: cordovil@math.ist.utl.pt URL: http://www.math.ist.utl.pt/\ rcordov Laboratoire de Recherche en Informatique UMR 8623, Batiment 490, Université Paris Sud, 91405 Orsay Cedex -- FRANCE E-mail: forge@lri.fr URL: http://www.lri.fr/\ forge Abstract: A family $\mathcal{C}_L$ of circuits of a matroid $M$ is a linear class if, given a modular pair of circuits in $\mathcal{C}_L$, any circuit contained in the union of the pair is also in $\mathcal{C}_L$. The pair $(M,\mathcal{C}_L)$ can be seen as a matroidal generalization of a biased graph. We introduce and study an Orlik--Solomon type algebra determined by $(M,\mathcal{C}_L)$. If $\mathcal{C}_L$ is the set of all circuits of $M$ this algebra is the Orlik--Solomon algebra of $M$. Keywords: arrangement of hyperplanes; matroid; Orlik--Solomon algebra; biased graphs. Classification (MSC2000): 05B35, 05Cxx, 14F40, 32S22. Full text of the article:
Electronic version published on: 7 Mar 2008.
© 2006 Sociedade Portuguesa de Matemática
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