A planar network proof for Hankel total positivity of type $B$ Narayana polynomials
Combinatorics
2021-07-23 v1
Abstract
The Hankel matrix of type B Narayana polynomials was proved to be totally positive by Wang and Zhu, and independently by Sokal. Pan and Zeng raised the problem of giving a planar network proof of this result. In this paper, we present such a proof by constructing a planar network allowing negative weights, applying the Lindstr\"om-Gessel-Viennot lemma and establishing an involution on the set of nonintersecting families of directed paths.
Keywords
Cite
@article{arxiv.2107.10608,
title = {A planar network proof for Hankel total positivity of type $B$ Narayana polynomials},
author = {Ethan Y. H. Li and Grace M. X. Li and Arthur L. B. Yang and Candice X. T. Zhang},
journal= {arXiv preprint arXiv:2107.10608},
year = {2021}
}
Comments
19 pages, 5 figures