Coxeter matroid polytopes |
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Authors: | Alexandre V Borovik Israel M Gelfand Neil White |
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Institution: | (1) Department of Mathematics, UMIST, P.O. Box 88, M60 1QD Manchester, UK;(2) Department of Mathematics, Rutgers University, 08903 New Brunswick, NJ, USA;(3) Department of Mathematics, University of Florida, 32611 Gainesville, FL, USA |
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Abstract: | If Δ is a polytope in real affine space, each edge of Δ determines a reflection in the perpendicular bisector of the edge.
The exchange groupW (Δ) is the group generated by these reflections, and Δ is a (Coxeter) matroid polytope if this group is finite. This simple
concept of matroid polytope turns out to be an equivalent way to define Coxeter matroids. The Gelfand-Serganova Theorem and
the structure of the exchange group both give us information about the matroid polytope. We then specialize this information
to the case of ordinary matroids; the matroid polytope by our definition in this case turns out to be a facet of the classical
matroid polytope familiar to matroid theorists.
This work was supported in part by NSA grant MDA904-95-1-1056. |
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Keywords: | 05B35 05E15 20F55 52B40 |
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