论文标题
关于$ q $ -laguerre多项式的线性化系数
On linearization coefficients of $q$-Laguerre polynomials
论文作者
论文摘要
经典laguerre polyenmials $ l_n（x）$的线性化系数$ \ MATHCAL {l_ {l_ {l_ {l_ {n_1}（x）\ dots l_ {n_k}（x））$的$等于$（N_1，n_1，n_k）$ -Derangements，允许，允许。 Kasraoui，Stanton和Zeng使用$ Q $ -Laguerre多项式和两个参数$ Q $和$ y $的$ Q $ -Analog。它们的公式表示$ q $ -laguerre多项式的线性化系数为$（n_1，\ dots，n_k）$的生成函数 - 两种统计信息的扰动，这些统计信息计算弱的毫无用处和交叉点。在本文中，通过在明显的完美匹配中构建签名的反向来证明其结果。
The linearization coefficient $\mathcal{L}(L_{n_1}(x)\dots L_{n_k}(x))$ of classical Laguerre polynomials $L_n(x)$ is known to be equal to the number of $(n_1,\dots,n_k)$-derangements, which are permutations with a certain condition. Kasraoui, Stanton and Zeng found a $q$-analog of this result using $q$-Laguerre polynomials with two parameters $q$ and $y$. Their formula expresses the linearization coefficient of $q$-Laguerre polynomials as the generating function for $(n_1,\dots,n_k)$-derangements with two statistics counting weak excedances and crossings. In this paper their result is proved by constructing a sign-reversing involution on marked perfect matchings.
