A Quasisymmetric Function Generalization of the Chromatic Symmetric Function
Keyword(s):
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.
2015 ◽
Vol DMTCS Proceedings, 27th...
(Proceedings)
◽
2014 ◽
Vol DMTCS Proceedings vol. AT,...
(Proceedings)
◽
1999 ◽
Vol 205
(1-3)
◽
pp. 229-234
◽
1993 ◽
Vol 112
(1-3)
◽
pp. 185-197
◽
2003 ◽
Vol Vol. 6 no. 1
◽