Immanant Positivity for Catalan-Stieltjes Matrices
Combinatorics
2021-06-25 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2106.12816,
title = {Immanant Positivity for Catalan-Stieltjes Matrices},
author = {Ethan Y. H. Li and Grace M. X. Li and Arthur L. B. Yang and Candice X. T. Zhang},
journal= {arXiv preprint arXiv:2106.12816},
year = {2021}
}
Comments
18 page, 4 figures