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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