An Orlik-Solomon type algebra for matroids with a fixed linear class of circuits

Details An Orlik-Solomon type algebra for matroids with a fixed linear class of circuits An Orlik-Solomon type algebra for matroids with a fixed linear class of circuits

2005-09-27

arxiv.org/abs/math/0509629v3

Mathematics

Combinatorics

10 pages. Port. Math. to appear

Scientific paper

A family C of circuits of a matroid M is a linear class if, given a modular pair of circuits in C}, any circuit contained in the union of the pair is also in C. The pair (M,C) can be seen as a matroidal generalization of a biased graph. We introduce and study an Orlik-Solomon type algebra determined by (M,C). If C is the set of all circuits of M this algebra is the Orlik-Solomon algebra of M.

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