Title: The Tutte Symmetric Function
| Speaker: | Logan Crew |
| Affiliation: | University of Waterloo |
| Zoom: | Please email Emma Watson |
Abstract:
The Tutte polynomial is one of the most celebrated and most well-studied graph functions, in part because it specializes to every graph polynomial with a linear deletion-contraction relation, such as the chromatic polynomial. In the 1990s, Stanley generalized the Tutte polynomial to a symmetric function, but at the cost of the deletion-contraction relation.
In this talk I will introduce these functions and then discuss the extended Tutte symmetric function, which is defined for graphs with positive integer vertex weights. I will illustrate how in this setting, the Tutte symmetric function regains important properties of the Tutte polynomial, including a deletion-contraction relation, and a universality property that it encompasses every nondegenerate symmetric function with a deletion-contraction relation on vertex-weighted graphs. We will also examine some properties of the extended Tutte symmetric function that generalize those of the Tutte polynomial.
This talk is based on joint work with Sophie Spirkl.