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- W3045932380 abstract "Many combinatorial numbers can be placed in the following generalized triangular array $[T_{n,k}]_{n,kge 0}$ satisfying the recurrence relation: begin{equation*} T_{n,k}=lambda(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)}{lambda}(n-k+1)T_{n-1,k-2} end{equation*} with $T_{0,0}=1$ and $T_{n,k}=0$ unless $0le kle n$ for suitable $a_0,a_1,a_2,b_0,b_1,b_2,d$ and $lambda$. For $ngeq0$, 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 $sum_{ngeq0}T_n(q)t^n$, 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." @default.
- W3045932380 created "2020-08-03" @default.
- W3045932380 creator A5091531217 @default.
- W3045932380 date "2020-07-29" @default.
- W3045932380 modified "2023-09-24" @default.
- W3045932380 title "Stieltjes moment properties and continued fractions from combinatorial triangles" @default.
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- W3045932380 doi "https://doi.org/10.48550/arxiv.2007.14924" @default.
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