论文标题
stieltjes瞬间特性和组合三角形的持续分数
Stieltjes moment properties and continued fractions from combinatorial triangles
论文作者
论文摘要
可以将许多组合数放在以下概括的三角数组$ [t_ {n，k}] _ {n，k \ ge 0} $满足复发关系的情况下：\ begin {equation {equation*} t_ {n，k} =λ（a_0n+a_1k+a_2）t_ {n-1，k}+（b_0n+b_0n+b_1k+b_2）t_ {n-1，k-1}+\ frac {d（da_1-b_1-b_1）}λ（n-k+1）λ（n-k+1）λ（n-k+1）λ（n-k+1）t_ n-equation n equation $ t_ {0,0} = 1 $和$ t_ {n，k} = 0 $，除非$ 0 \ le k \ le n $用于合适的$ a_0，a_1，a_1，a_2，b_0，b_1，b_1，b_1，b_2，d $和$λ$。对于$ n \ geq0 $，用$ t_n（q）$表示$ n $ th行的生成功能。在本文中，我们为$ \ textbf {x} $ - stieltjes mist属性和$ 3 $ - $ \ textbf {x} $ - 基于$ t_n（q）$的log-convexity制定了各种标准。由$ Q $和复发关系中发生的那些参数组成的不确定的。借助王和朱的标准[adv。在应用中。数学。 （2016）]，我们表明$ t_ {n，k} $的相应线性变换保留了序列的stieltjes矩属性。最后，我们提出了一些相关的示例，包括阶乘数字，惠特尼数字，斯特林排列，微型树木和峰值统计。
Many combinatorial numbers can be placed in the following generalized triangular array $[T_{n,k}]_{n,k\ge 0}$ satisfying the recurrence relation: \begin{equation*} T_{n,k}=λ(a_0n+a_1k+a_2)T_{n-1,k}+(b_0n+b_1k+b_2)T_{n-1,k-1}+\frac{d(da_1-b_1)}λ(n-k+1)T_{n-1,k-2} \end{equation*} with $T_{0,0}=1$ and $T_{n,k}=0$ unless $0\le k\le n$ for suitable $a_0,a_1,a_2,b_0,b_1,b_2,d$ and $λ$. For $n\geq0$, denote by $T_n(q)$ the generating function of the $n$-th row. In this paper, we develop various criteria for $\textbf{x}$-Stieltjes moment property and $3$-$\textbf{x}$-log-convexity of $T_n(q)$ based on the Jacobi continued fraction expression of $\sum_{n\geq0}T_n(q)t^n$, where $\textbf{x}$ is a set of indeterminates consisting of $q$ and those parameters occurring in the recurrence relation. With the help of a criterion of Wang and Zhu [Adv. in Appl. Math. (2016)], we show that the corresponding linear transformation of $T_{n,k}$ preserves Stieltjes moment properties of sequences. Finally, we present some related examples including factorial numbers, Whitney numbers, Stirling permutations, minimax trees and peak statistics.
