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On Matroids and Orlik-Solomon Algebras
Yukihito Kawahara
Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi Tokyo 192-0397, Japan
ykawa@comp.metro-u.ac.jp
Annals of Combinatorics 8 (1) p.63-80 March, 2004
AMS Subject Classification: 03B35, 13D03, 52C35
Abstract:
In this paper we axiomatize combinatorics of arrangements of affine hyperplanes, which is a generalization of matroids, called quasi-matroids. We show that quasi-matroids are equivalent to pointed matroids. On the other hand, the Orlik-Solomon (OS) algebra of a quasi-matroid can be constructed. We prove that the OS algebra of a quasi-matroid is isomorphic to the direct image of the OS algebra of a matroid by the linear derivation.
Keywords: matroid, geometric lattice, geometric semilattice, Orlik-Solomon algebra, hyperplane arrangement

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