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

Arthur L.B. Yang; Candice X.T. Zhang; Ethan Y.H. Li; Grace M.X. Li

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

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arxiv 2107.10608 v1 pith:5ELRUGED submitted 2021-07-22 math.CO

Ethan Y.H. Li , Grace M.X. Li , Arthur L.B. Yang , Candice X.T. Zhang This is my paper

classification math.CO

keywords networkplanarproofhankelnarayanapolynomialstypeallowing

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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.

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