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


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.

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