The chromatic symmetric function $X_G$ of a graph $G$ was introduced byStanley. In this paper we introduce a quasisymmetric generalization $X^k_G$called the $k$-chromatic quasisymmetric function of $G$ and show that it ispositive in the fundamental basis for the quasisymmetric functions. Followingthe specialization of $X_G$ to $\chi_G(\lambda)$, the chromatic polynomial, wealso define a generalization $\chi^k_G(\lambda)$ and show that evaluations ofthis polynomial for negative values generalize a theorem of Stanley relatingacyclic orientations to the chromatic polynomial.
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机译：图$ G $的色对称函数$ X_G $由Stanley引入。在本文中，我们介绍了一种称为$ G $的准对称泛化$ X ^ k_G $，它是准对称函数的基本基础。在将$ X_G $专门化为彩色多项式$ \ chi_G（\ lambda）$之后，我们还定义了泛化$ \ chi ^ k_G（\ lambda）$并表明对负值的此多项式求值可以推广与循环方向相关的Stanley定理到色多项式。
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