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arXiv · 2107.10608

A planar network proof for Hankel total positivity of type $B$ Narayana polynomials

Ethan Y. H. Li·Grace M. X. Li·Arthur L. B. Yang·Candice X. T. Zhang
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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 Lindström-Gessel-Viennot lemma and establishing an involution on the set of nonintersecting families of directed paths.

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Ethan Y. H. Li, Grace M. X. Li, Arthur L. B. Yang, Candice X. T. Zhang. 2021-07-22. A planar network proof for Hankel total positivity of type $B$ Narayana polynomials. https://arxiv.org/abs/2107.10608

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