Annals of Combinatorics 1 (1997) 17-26
The Lattice of Flats and its Underlying Flag Matroid Polytope
Alexandre V. Borovik 1, Israel M. Gelfand2, Andrew Vince3, and Neil White3
1Department of Mathematics, UMIST, P.O. Box 88, Manchester M60 1QD, UK
2Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA
3Department of Mathematics, University of Florida, Gainesville, FL 32611, USA
Received October 3, 1996
AMS Subject Classification: 05B35, 05E15, 20F55, 52B40
Abstract. Let M be a matroid and F the collection of all linear orderings of bases of M, or flags of M. We define the flag matroid polytope Δ (F). We determine when two vertices of Δ (F) are adjacent, and provide a bijection between maximal chains in the lattice of flats of M and certain maximal faces of Δ (F).
Keywords: matroid, Coxeter matroid, flag matroid, flag matroid polytope
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