Abstracts
for the Seminar

Spring 2022

**Speaker: **Jesse Selover, UMass Amherst

**Title: **On the Newton Polytopes of Chromatic Symmetric Functions

**Time:** 2:30 PM, Monday, April 18, 2022

**Place:** Zoom

**Abstract:** The chromatic symmetric function, introduced by Stanley, is a well-studied generalization of the chromatic polynomial of a graph. Chromatic symmetric functions of (3+1)-free incomparability graphs (in particular, incomparability graphs of unit interval orders) are of particular interest. Motivated by the Stanley-Stembridge conjecture that such chromatic functions are e-positive, we show that the allowable coloring weights for such a graph are the lattice points of a permutahedron, and give a formula for the dominant coloring weight. We also give conjectures about convexity properties of these symmetric functions, and prove that they are Lorentzian in the abelian case.
This is joint work with Alejandro Morales and Jacob Matherne.

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