Geodesic
A quasisymmetric function generalization of the chromatic symmetric function
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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The chromatic symmetric function $X_G$ of a graph $G$ was introduced by Stanley. In this paper we introduce a quasisymmetric generalization $X^k_G$ called the $k$-chromatic quasisymmetric function of $G$ and show that it is positive in the fundamental basis for the quasisymmetric functions. Following the specialization of $X_G$ to $\chi_G(\lambda)$, the chromatic polynomial, we also define a generalization $\chi^k_G(\lambda)$ and show that evaluations of this polynomial for negative values generalize a theorem of Stanley relating acyclic orientations to the chromatic polynomial.
DOI : 10.37236/518
Classification : 05C31, 05E05 
@article{10_37236_518,
     author = {Brandon Humpert},
     title = {A quasisymmetric function generalization of the chromatic symmetric function},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/518},
     zbl = {1213.05133},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/518/}
}
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Brandon Humpert. A quasisymmetric function generalization of the chromatic symmetric function. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/518

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