Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 Fall 2016

Speaker:  Alex Fink, Queen Mary University of London
Title: The Tutte polynomial via lattice point enumeration
Time: 2:30 PM, Monday, Nov 21, 2016
Place:  Malott 206

Abstract: Tamás Kálmán discovered a pair of univariate polynomials associated to a hypergraph which enumerate its spanning trees by internal and external activity. In joint work with Amanda Cameron, we have extended this to a bivariate polynomial of polymatroids enumerating both activity statistics at once, using lattice point enumeration. On matroids we find that our invariant agrees with the Tutte polynomial, though not in its most obvious basis, and that its coefficients have combinatorial meaning closely tied to the Dawson partition. I will close by speculating on relationships to algebro-geometric constructions for Tutte and related invariants.

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