Georgia Institute of Technology College of Sciences

 Every graph is associated to a symmetric function constructed from proper colorings of the graph.  The Stanley-Stembridge conjecture posits that the expansion of the chromatic symmetric function into the elementary symmetric functions has positive coefficients for a certain class of graphs.  We explore a potential new approach to the Stanley-Stembridge Conjecture using combinatorial objects called "special rim hooks" and connect this to the "chromatic quasisymmetric functions" introduced by Shareshian and Wachs as a generalization of chromatic symmetric functions.  This is joint work with Meagan Hodge.