Abstract: The chromatic symmetric function, introduced by Stanley, is a well-studied graph invariant generalizing the chromatic polynomial. Chromatic symmetric functions of (3+1)-free incomparability graphs (including indifference graphs) are of particular interest in algebraic combinatorics. Motivated by the Stanley-Stembridge conjecture that such chromatic symmetric functions are e-positive, we show that the weights of colorings of an indifference graph form a permutahedron, and give a formula for the maximal coloring weight in dominance order. We also give conjectures about convexity properties of these symmetric functions, and prove that they are Lorentzian in the case of abelian indifference graphs. This is joint work with Alejandro Morales and Jacob Matherne.
The CICS Theory Seminar is free and open to the public. If you are interested in giving a talk, please email Cameron Musco or Rik Sengupta. Note that in addition to being a public lecture series, this is also a one-credit graduate seminar (CompSci 891M) that can be taken repeatedly for credit.