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 Lindstrom-Gessel-Viennot lemma and establishing an involution on the set of nonintersecting families of directed paths.
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