论文标题
Dyck路径和Q-Rook理论的色度对称功能（扩展摘要）
Chromatic symmetric functions of Dyck paths and q-rook theory (extended abstract)
论文作者
论文摘要
Stanley及其Shareshian-Wachs $ Q $ -Analogue的Dyck路径的色度对称功能（CSF）具有与Hessenberg品种，对角线谐波和LLT多项式的重要连接。对于所谓的Abelian Dyck路径，它们也与Stanley-Stumbridge（1993）和Guay-Paquet（2013）的结果相关的奇怪的是与非攻击的roks的位置相关。对于$ q $ - analogue，这些结果已由Abreu-Nigro（2020）和Guay-Paquet（私人通信）（使用$ Q $ hit数字）推广，这些数字是Garsia和Remmel引入的变体。我们的主要结果之一是瓜伊·帕奎特（Guay-Paquet）优雅的身份的新证明，它以$ q $ hit系数的CSF为基础表达$ Q $ -CSF。我们进一步显示了它与基本对称函数中$ q $ -CSF扩展的Abreu-Nigro身份的等效性。 这是FPSAC扩展抽象版本。完整版本在Arxiv：2104.07599。
The chromatic symmetric function (CSF) of Dyck paths of Stanley and its Shareshian-Wachs $q$-analogue have important connections to Hessenberg varieties, diagonal harmonics, and LLT polynomials. In the case of, so-called, abelian Dyck paths they are also curiously related to placements of non-attacking rooks by results of Stanley-Stembridge (1993) and Guay-Paquet (2013). For the $q$-analogue, these results have been generalized by Abreu-Nigro (2020) and Guay-Paquet (private communication), using $q$-hit numbers, which are a variant of the ones introduced by Garsia and Remmel. Among our main results is a new proof of Guay-Paquet's elegant identity expressing the $q$-CSFs in a CSF basis with $q$-hit coefficients. We further show its equivalence to the Abreu-Nigro identity expanding the $q$-CSF in the elementary symmetric functions. This is the FPSAC extended abstract version. The full version is at ArXiv: 2104.07599.
