Victor Reiner, U. of Minnesota
A quasisymmetric function for matroids
(joint work with Lou Billera)

Various combinatorial Hopf algebras have recently grown in popularity, including Gessel's algebra of quasisymmetric functions, and a Hopf algebra of matroids studied by Crapo and Schmitt.

This talk will describe a connection between these two Hopf algebras, via a new matroid invariant in the form of a quasisymmetric function. This turns out to define a Hopf morphism between the algebras, with some other pleasant properties. In particular, it has an interesting application to the subtle question of when one matroid basis polytope can be decomposed into a union of other matroid basis polytopes.