论文标题
衍生品，欧拉（Eulerian）多项式和$ g $ indexes of Young Tableaux
Derivatives, Eulerian polynomials and the $g$-indexes of Young tableaux
论文作者
论文摘要
在本文中，我们首先介绍了$ k $ order eulerian多项式和$ 1/k $ -eulerian多项式的总和公式。然后，我们在反转序列以及$ k $ -young tableaux方面提出了$（c（x）d）^n $的组合扩展，其中$ c（x）$是不确定的$ x $和$ d $的可区分功能，是相对于$ x $的衍生产品。我们定义了$ g $ indexes的$ k $ -young tableaux和Young Tableaux，它们在组合中具有重要的应用。通过建立$ k $ -young tableaux和标准的年轻tableaux之间的某些关系，我们表达了欧拉尔式的多项式，二阶欧拉尔式多项式，安德烈·多项式和多项式的产生多项式的多项式eulererian eulererian多项式的多项式在标准的Young Tableaux中，这些都与这些polyn pynomiss相关。
In this paper we first present summation formulas for $k$-order Eulerian polynomials and $1/k$-Eulerian polynomials. We then present combinatorial expansions of $(c(x)D)^n$ in terms of inversion sequences as well as $k$-Young tableaux, where $c(x)$ is a differentiable function in the indeterminate $x$ and $D$ is the derivative with respect to $x$. We define the $g$-indexes of $k$-Young tableaux and Young tableaux, which have important applications in combinatorics. By establishing some relations between $k$-Young tableaux and standard Young tableaux, we express Eulerian polynomials, second-order Eulerian polynomials, André polynomials and the generating polynomials of gamma coefficients of Eulerian polynomials in terms of standard Young tableaux, which imply a deep connection among these polynomials.
