Planar networks and total positivity of Riordan arrays
Combinatorics
2025-12-15 v1
Abstract
In 2015, Chen, Liang and Wang provided several sufficient conditions for the total positivity of Riordan arrays and asked for combinatorial proofs of these results. In this paper, we present such proofs by constructing suitable planar networks with non-negative weights and applying the Lindstr\"om-Gessel-Viennot lemma. Moreover, we slightly generalize one of the results and give more totally positive Riordan arrays.
Keywords
Cite
@article{arxiv.2512.11419,
title = {Planar networks and total positivity of Riordan arrays},
author = {Lanqi Du and Ethan Y. H. Li},
journal= {arXiv preprint arXiv:2512.11419},
year = {2025}
}
Comments
12 pages, 3 figures