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Immanant Positivity for Catalan-Stieltjes Matrices

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arxiv 2106.12816 v1 pith:EF3GR3AY submitted 2021-06-24 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 matricespolynomialscatalan-stieltjesconditionssufficientapplicationscombinatorialconstruct
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In this paper we give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices. To obtain these sufficient conditions, we construct new planar networks with a recursive nature for Catalan-Stieltjes matrices. As applications, we provide a unified way to produce inequalities for many combinatorial polynomials, such as the Eulerian polynomials, Schr\"{o}der polynomials and Narayana polynomials.

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