2021/07/22 by Ethan Y. H. Li, Li, Ethan Y. H., Grace M. X. Li +5 · 1 citation
Computer Science · Mathematics · #05A15 #05A19 #05A20 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2107.10608
openalex publication_date 2021/07/22 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28
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.