Yet another criterion for the total positivity of Riordan arrays
Combinatorics
2021-07-20 v1
Abstract
Let be a Riordan array, where and . We show that if the matrix \begin{equation*} \left[\begin{array}{ccccc} d_0 & h_0 & 0 & 0 &\cdots\\ d_1 & h_1 & h_0 & 0 &\\ d_2 & h_2 & h_1 & h_0 &\\ \vdots&\vdots&&&\ddots \end{array}\right] \end{equation*} is totally positive, then so is the Riordan array .
Cite
@article{arxiv.2107.08436,
title = {Yet another criterion for the total positivity of Riordan arrays},
author = {Jianxi Mao and Lili Mu and Yi Wang},
journal= {arXiv preprint arXiv:2107.08436},
year = {2021}
}