Title: An Ehrhart theory generalisation of the Tutte polynomial
Abstract: The Tutte polynomial is one of the most important and
well-known graph polynomials, and also features prominently in
matroid theory. It is however not directly applicable to
polymatroids, these being a natural generalisation of matroids.
For instance, deletion-contraction properties do not hold. We
construct a polynomial for polymatroids which behaves similarly
to the Tutte polynomial of a matroid, and in fact contains the
same information as the Tutte polynomial when we restrict to
matroids. This is joint work with Alex Fink.