论文标题
色度对称功能和逆Kostka矩阵的$ e $ - 积极性
The $e$-positivity of the chromatic symmetric functions and the inverse Kostka matrix
论文作者
论文摘要
我们使用在Eğecioğlu-Remmel（1990）中研究的Kostka矩阵倒数的组合解释来扩展基本对称函数中弹跳数字第三的染色函数。我们证明，在此扩展中的某些系数是积极的。我们建立了$ e $ $ - 积极性的一类扩展类的色度对称功能，用于弹跳的第三次抗曲路径，而不是Cho-Huh（2019）的“钩形”案例。
We expand the chromatic symmetric functions for Dyck paths of bounce number three in the elementary symmetric function basis using a combinatorial interpretation of the inverse of the Kostka matrix studied in Eğecioğlu-Remmel (1990). We prove that certain coefficients in this expansion are positive. We establish the $e$-positivity of an extended class of chromatic symmetric functions for Dyck paths of bounce number three beyond the "hook-shape" case of Cho-Huh (2019).
