A planar network proof for Hankel total positivity of type \(B\) Narayana polynomials

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 w...

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Bibliographic Details
Published in:arXiv.org 2021-07
Main Authors: Li, Ethan Y H, Li, Grace M X, Yang, Arthur L B, Zhang, Candice X T
Format: Article
Language:English
Subjects:
Hankel matrices
Polynomials
Online Access:Get full text
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Summary: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.
ISSN:2331-8422