**UM Math Graduate Students Seminar**

Brittney Ellzey

* University of Miami *

**will present**

**Graph Colorings and Symmetric Functions**

Friday, March 20, 2015, 3:30pm

Ungar Building Room 402

**Abstract: **

A proper coloring of a graph is a map that assigns a color to each vertex with the condition that vertices connected by an edge are assigned different colors. Given a nonnegative integer k, the chromatic polynomial counts the number of proper colorings of a graph that use at most k colors. Stanley introduces the chromatic symmetric function of a graph, which generalizes the chromatic polynomial of a graph. Shareshian and Wachs generalize this further to the chromatic quasisymmetric function of a graph. We will look at some examples to get a better idea of what these objects are. We will also look at a few theorems and conjectures about the chromatic symmetric function and their generalizations to the chromatic quasisymmetric function. We will then see how these theorems apply to our examples.

Back to the seminar's page