University of Minnesota Combinatorics Seminar
Friday, March 26, 2010
3:35pm in 570 Vincent Hall



The rank partition of a matroid

Andy Berget

Univ. of California - Davis


Abstract

The rank partition measures how close a matroid is to being a union of bases. I will discuss how this invariant arises using representation theory. I will show how representation theory allows us to prove that a matroid which is weak order minimal with a given rank partition has finitely many realizations, up to projective equivalence. The main idea behind the proof is the use of matroid base polytope decompositions arising from torus orbit closures in Grassmannians.