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Valuations for Matroid Polytope Subdivisions

  Published:2010-07-29
 Printed: Dec 2010
  • Federico Ardila,
    San Francisco State University, San Francisco, CA, USA
  • Alex Fink,
    University of California, Berkeley, Berkeley, CA, USA
  • Felipe Rincón,
    Universidad de Los Andes, Bogotá, Colombia
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Abstract

We prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.
MSC Classifications: 05B35, 52B40, 52B45, 52C22 show english descriptions Matroids, geometric lattices [See also 52B40, 90C27]
Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx]
Dissections and valuations (Hilbert's third problem, etc.)
Tilings in $n$ dimensions [See also 05B45, 51M20]
05B35 - Matroids, geometric lattices [See also 52B40, 90C27]
52B40 - Matroids (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) [See also 05B35, 52Cxx]
52B45 - Dissections and valuations (Hilbert's third problem, etc.)
52C22 - Tilings in $n$ dimensions [See also 05B45, 51M20]
 

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