The University of Michigan Combinatorics Seminar
Winter 2009
January 30, 4:10-5:00, 3866 East Hall

Valuations for matroid subdivisions

Alex Fink

UC Berkeley


Subdivisions of matroid polytopes have made appearances in several combinatorial and algebraic contexts. An interesting class of functions on matroids, first investigated by Billera, Jia & Reiner and Speyer, are those that are valuative: a function is valuative if it behaves well in subdivisions, i.e., factors through the map from matroids to the group of the polyhedral algebra. Several well-known matroid invariants are valuative. Derksen has conjectured, and since proved, that a certain set of matroid invariants generate all S_n-symmetric valuative functions, and the conjecture readily extends to the nonsymmetric case. I'll present a mostly independent proof of this conjecture, and discuss some other valuative functions.

Knowledge of matroids will not be assumed. Parts of this work are joint separately with Felipe Rincon and Federico Ardila, and with David Speyer.