A quasisymmetric function generalization of the chromatic symmetric\n function

2010/04/15 by Brandon Humpert, Humpert, Brandon
Mathematics · #Advanced Combinatorial Mathematics

paper · pdf · doi:10.48550/arxiv.1004.2685

Abstract

The chromatic symmetric function X_G of a graph G was introduced by\nStanley. In this paper we introduce a quasisymmetric generalization X^k_G\ncalled the k-chromatic quasisymmetric function of G and show that it is\npositive in the fundamental basis for the quasisymmetric functions. Following\nthe specialization of X_G to \χ_G(\λ), the chromatic polynomial, we\nalso define a generalization \χ^k_G(\λ) and show that evaluations of\nthis polynomial for negative values generalize a theorem of Stanley relating\nacyclic orientations to the chromatic polynomial.\n

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