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]

top of page | contact us | social media | privacy | site map