English

Yet another criterion for the total positivity of Riordan arrays

Combinatorics 2021-07-20 v1

Abstract

Let R=R(d(t),h(t))R=\mathcal{R}(d(t),h(t)) be a Riordan array, where d(t)=n0dntnd(t)=\sum_{n\ge 0}d_nt^n and h(t)=n0hntnh(t)=\sum_{n\ge 0}h_nt^n. 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 RR.

Keywords

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}
}