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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Borovik, A., Vince, A. An Adjacency Criterion for Coxeter Matroids. Journal of Algebraic Combinatorics 9, 271–280 (1999). https://doi.org/10.1023/A:1018600303418
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DOI: https://doi.org/10.1023/A:1018600303418