A categorification of the chromatic symmetric function

摘要

AbstractThe Stanley chromatic symmetric functionXGof a graphGis a symmetric function generalization of the chromatic polynomial and has interesting combinatorial properties. We apply the ideas from Khovanov homology to construct a homology theory of gradedSn-modules, whose graded Frobenius seriesFrobG(q,t)specializes to the chromatic symmetric function atq=t=1. This homology theory can be thought of as a categorification of the chromatic symmetric function, and it satisfies homological analogues of several familiar properties ofX