Immanant positivity for Catalan-Stieltjes matrices

Abstract

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, Schröder polynomials, and Narayana polynomials.

Key words： Immanant; character; Catalan-Stieltjes matrices; Hankel matrices; planar network

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