The Tutte polynomial via lattice point counting
Combinatorics
2018-02-28 v1
Abstract
We recover the Tutte polynomial of a matroid, up to change of coordinates, from an Ehrhart-style polynomial counting lattice points in the Minkowski sum of its base polytope and scalings of simplices. Our polynomial has coefficients of alternating sign with a combinatorial interpretation closely tied to the Dawson partition. Our definition extends in a straightforward way to polymatroids, and in this setting our polynomial has K\'alm\'an's internal and external activity polynomials as its univariate specialisations.
Cite
@article{arxiv.1802.09859,
title = {The Tutte polynomial via lattice point counting},
author = {Amanda Cameron and Alex Fink},
journal= {arXiv preprint arXiv:1802.09859},
year = {2018}
}