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Universality for valuations of (poly)matroid polytope decompositions

Algebra & Discrete Mathematics

Speaker: Alexander Fink, UC Berkeley
Location: 2112 MSB
Start time: Fri, Dec 4 2009, 4:10PM

Many important matroid and polymatroid invariants are valuations of polytope decompositions. We construct explicit bases for the modules of matroids and polymatroids on a fixed ground set modulo relations given by decompositions, and their duals, the modules of valuations on (poly)matroid base polytopes. The basis elements for matroid polytopes are essentially the Schubert matroids. We also discuss some variants of this basic problem.

This work is joint with Harm Derksen.