Lollipop and lariat symmetric functions

Samantha Dahlberg, Stephanie van Willigenburg

Published 2017-02-22Version 1

We compute an explicit $e$-positive formula for the chromatic symmetric function of a lollipop graph, $L_{m,n}$. From here we deduce that there exist countably infinite nonisomorphic $e$-positive, and hence Schur-positive, bases of the algebra of symmetric functions. Finally, we resolve 6 conjectures on the chromatic symmetric function of a lariat graph, $L_{n+3}$.