Speaker
Description
R. Stanley introduced the chromatic symmetric functions of a graph $G$. This definition was later refined by J. Shareshian and M. Wachs, where a parameter $q$ is introduced in the definition of chromatic uasisymmetric functions. In this talk, we discuss two separate results and their connection: (1) a Hall-Littlewood expansion of the chromatic quasisymmetric functions (2) $e$-positivity of the chromatic quasisymmetric functions when a partition $\lambda$ indexing the elementary symmetric function is a hook shape. To explain both results we introduce "linked" rook placements, where each column and row of a board contain at most one rook and some of rooks are linked. we also discuss other $e$-positivity results and relationship with LLT polynomials. (1) is based on joint work with Meesue Yoo and (2) is with Jeong Hyun Sung.
