MIT Combinatorics Seminar

A quasisymmetric function for matroids

Vic Reiner  (University of Minnesota)

Wednesday, March 07, 2007    4:15 pm    Room 2-136


I'll describe a new invariant of matroids that takes the form of a quasisymmetric function, then describe some of its pleasant properties. One is that it defines a morphism between two known combinatorial Hopf algebras. Another is that it helps answer a subtle question that arises in work of Kapranov, Lafforgue, Hacking, Keel, Tevelev and others: when does a matroid polytope decompose into smaller matroid polytopes? Knowledge of quasisymmetric functions will not be assumed.

This is joint work with Lou Billera and Ning Jia.