Annals of Combinatorics 1 (1997) 173-181

A Geometric Characterization of Coxeter Matroids

V.V. Serganova, A. Vince, and A. Zelevinsky

Department of Mathematics, University of California, Berkeley, CA 94720, USA

Department of Mathematics, University of Florida, Gainesville, FL 32611, USA

Department of Mathematics, Northeastern University, Boston, MA 02115, USA

Received February 11, 1997

AMS Subject Classification: 05E99, 05B35, 20F55

Abstract.Coxeter matroids, introduced by Gelfand and Serganova, are combinatorial structures associated with any finite Coxeter group and its parabolic subgroup; they include ordinary matroids as a special case. A basic result in the subject is a geometric characterization of Coxeter matroids, first stated by Gelfand and Serganova. This paper presents a self-contained, simple proof of a more general version of this geometric characterization.

Keywords: matroid, Coxeter group, Coxeter matroid, Bruhat order


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