Algebraic & Enumerative Combinatorics - Laura Pierson

Title: Two variations of the chromatic symmetric function

Abstract: The /chromatic symmetric function/ is a symmetric function generalization of the chromatic polynomial that encodes the ways to color a graph such that no two adjacent vertices get the same color. We will discuss two different analogues of the chromatic symmetric function: a K-theoretic analogue called the /Kromatic symmetric function/, and a categorification called the /chromatic symmetric homology/. We show that certain properties of a graph can be recovered given its Kromatic symmetric function, and we give some formulas for special cases of the chromatic symmetric homology.