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The lattice of flats and its underlying flag matroid polytope

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Abstract

LetM be a matroid andF the collection of all linear orderings of bases ofM, orflags ofM. 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 ofM and certain maximal faces of Δ(F).

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Authors and Affiliations

  1. Department of Mathematics, UMIST, P.O. Box 88, M60 1QD, Manchester, UK

    Alexandre V. Borovik

  2. Department of Mathematics, Rutgers University, 08903, New Brunswick, NJ, USA

    Israel M. Gelfand

  3. Department of Mathematics, University of Florida, 32611, Gainesville, FL, USA

    Andrew Vince & Neil White

Authors
  1. Alexandre V. Borovik
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  2. Israel M. Gelfand
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  3. Andrew Vince
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  4. Neil White
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Supported in part by NSA grant MDA904-95-1-1056.

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Borovik, A.V., Gelfand, I.M., Vince, A. et al. The lattice of flats and its underlying flag matroid polytope. Annals of Combinatorics 1, 17–26 (1997). https://doi.org/10.1007/BF02558461

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  • DOI: https://doi.org/10.1007/BF02558461

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