A lattice point counting generalisation of the Tutte polynomial
The Tutte polynomial for matroids is not directly applicable to polymatroids. For instance, deletioncontraction 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 polynomial is constructed using lattice point counts in the Minkowski sum of the base polytope of a polymatroid and scaled copies of the standard simplex. We also show that, in the matroid case, our polynomial has coefficients of alternating sign, with a combinatorial interpretation closely tied to the Dawson partition.
AuthorsCameron, A; Fink, A; Formal Power Series and Algebraic Combinatorics 2016
- College Publications