Algebraic and Enumerative Combinatorics Seminar | Shao Yuan Lin, Distinguishability and linear independence for H-chromatic symmetric functions

Abstract: We study the H-chromatic symmetric functions X_G^H introduced by Eagles et al. (2022), which generalizes the chromatic symmetric function X_G to the context of H-colorings, which tracks graph homomorphisms G → H. We first show that self-chromatic symmetric functions X_G^G determine quantities like the connected components of a forest and the degree sequence of a caterpillar. We then show that the X_G^H's form a basis of the symmetric function ring for certain collections of (G,H), such as the self-CSFs of complete multipartite graphs. Lastly, we define and discuss H-chromatic polynomials as specializations of H-CSFs. This is joint work with Laura Pierson.

There will be a pre-seminar presenting relevant background at beginning graduate level starting at 1:30pm in MC 5417.