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
serganov@math.berkeley.edu

Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
vince@math.ufl.edu

Department of Mathematics, Northeastern University, Boston, MA 02115, USA
andrei@neu.edu

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


References

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