Colorings and positivity
Tid: On 2017-02-08 kl 10.15 - 11.15
Plats: Room 3418, Math department, KTH
Medverkande: Per Alexandersson, KTH
Abstract
We study a version of Stanley's chromatic symmetric polynomials.
For unit interval graphs, Shareshian and Wachs introduced a refined
version with an extra parameter 'q'.
We show that many of the positivity problems regarding this family of
polynomials have analogues for unicellular LLT polynomials.
In particular, we formulate an e-positivity conjecture analogous to that
of Stanley and Stembridge.
We prove both versions of this conjecture for the path and cycle graph,
by giving an explicit e-expansion.