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Universality for valuations of (poly)matroid polytope decompositionsAlgebra & 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.