论文标题
彩色的准对称函数和非交易性$ p $ - 符合对称功能
Chromatic quasisymmetric functions and noncommutative $P$-symmetric functions
论文作者
论文摘要
对于自然单位间隔订单$ p $，我们描述了$ p $的无与伦比的适当颜色。我们还在堆上引入了一个称为\ emph {local flip}的组合操作。该操作定义了适当的着色的等价关系，而等效关系完善了Shareshian和Wachs介绍的上升统计量。 此外，我们定义了Fomin和Greene在$ p $方面引入的非共同对称函数的类似物。我们在$ p $的色度准对称函数与这些非交换对称函数之间建立了二元性。这种二元性使我们呈色度准对称函数的正膨胀到几个对称函数库中。特别是，我们为$ e $ - 积极性猜想提供了一些部分结果。
For a natural unit interval order $P$, we describe proper colorings of the incomparability graph of $P$ in the language of heaps. We also introduce a combinatorial operation, called a \emph{local flip}, on the heaps. This operation defines an equivalence relation on the proper colorings, and the equivalence relation refines the ascent statistic introduced by Shareshian and Wachs. In addition, we define an analogue of noncommutative symmetric functions introduced by Fomin and Greene, with respect to $P$. We establish a duality between the chromatic quasisymmetric function of $P$ and these noncommutative symmetric functions. This duality leads us to positive expansions of the chromatic quasisymmetric functions into several symmetric function bases. In particular, we present some partial results for the $e$-positivity conjecture.
