Discrete Math Seminar: Jair Taylor

  • Date: 09/22/2015
  • Time: 16:00
Jair Taylor, 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.

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Location: ESB 4127