Alex Fink: The Tutte polynomial via lattice point enumeration

Abstract

I will explain how to recover the Tutte polynomial of a matroid from
an Ehrhart-style polynomial which counts lattice points in Minkowski
sums of simplices and its base polytope. The key ingredient is a
polyhedral interpretation of activity; along the way, this will give
us a regular subdivision whose cells naturally encode Dawson's
activity partition. I will also talk about its generalisation to
polymatroids: in this setting, finding a bivariate activity invariant
was a question of Tam\'as K\'alm\'an, who constructed the univariate
activity invariant in his work on enumerating spanning trees of
hypergraphs.

This is joint work with Amanda Cameron (MPI Leipzig).