Abstract
Let G be a graph, and let χG be its chromatic polynomial. For any non-negative integers i,j, we give an interpretation for the evaluation χG(i)(−j) in terms of acyclic orientations. This recovers the classical interpretations due to Stanley and to Greene and Zaslavsky respectively in the cases i=0 and j=0. We also give symmetric function refinements of our interpretations, and some extensions. The proofs use heap theory in the spirit of a 1999 paper of Gessel.
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