An Adjacency Criterion for Coxeter Matroids |
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Authors: | Alexandre Borovik Andrew Vince |
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Institution: | (1) UMIST, Department of Mathematics, P.O. Box 88, Manchester, M60 1QD, UK;(2) Department of Mathematics, University of Florida, Gainesville, FL, 32611 |
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Abstract: | A Coxeter matroid is a generalization of matroid, ordinary matroid being the case corresponding to the family of Coxeter groups A
n
, which are isomorphic to the symmetric groups. A basic result in the subject is a geometric characterization of Coxeter matroid in terms of the matroid polytope, a result first stated by Gelfand and Serganova. This paper concerns properties of the matroid polytope. In particular, a criterion is given for adjacency of vertices in the matroid polytope. |
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Keywords: | matroid Coxeter matroid Coxeter group matroid polytope |
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