## Discrete Math Seminar: Jair Taylor

- Date: 09/22/2015
- Time: 16:00

*University of Washington*

University of British Columbia

Chromatic symmetric functions of hypertrees

The chromatic symmetric function $X_H$ of a hypergraph $H$ is the generating function for all colorings of $H$ so that no edge is monochromatic. When $H$ is an ordinary graph, it is known that $X_H$ is positive in the fundamental quasisymmetric functions $F_S$, but this is not the case for general hypergraphs. We exhibit a class of hypergraphs $H$ --- hypertrees with prime-sized edges --- for which $X_H$ is $F$-positive, and give an explicit combinatorial interpretation for the $F$-coefficients of $X_H$. We also present a conjecture that certain chromatic symmetric functions of hypergraphs are Schur-positive.

Location: ESB 4127