A Large Class of Conjecturally Stable Chromatic Symmetric Functions

The theory of stable and Lorentzian polynomials has recently found a number of successes in a variety of research areas including combinatorics, engineering, and computer science; in particular, they have played a key role in solving long-standing open problems such as the Kadison–Singer problem and Mason’s log-concavity conjecture. More recently, the classes of stable polynomials and Lorentzian polynomials have appeared in representation theory, algebraic combinatorics, and even knot theory. We further highlight their ubiquity by introducing a large class of chromatic symmetric functions related to Hessenberg varieties and the Stanley–Stembridge conjecture that are conjecturally Lorentzian and stable.