Immanant positivity for Catalan-Stieltjes matrices

doi:10.1007/s11464-021-0977-7

Front. Math. China

2022, Vol. 17

Issue (5) : 887-903 https://doi.org/10.1007/s11464-021-0977-7

RESEARCH ARTICLE

Immanant positivity for Catalan-Stieltjes matrices

Ethan Y. H. LI, Grace M. X. LI, Arthur L. B. YANG(

), Candice X. T. ZHANG

Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, China

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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.

Keywords Immanant character Catalan-Stieltjes matrices Hankel matrices planar network

Corresponding Author(s): Arthur L. B. YANG

Issue Date: 28 December 2022

Cite this article:

Ethan Y. H. LI,Grace M. X. LI,Arthur L. B. YANG, et al. Immanant positivity for Catalan-Stieltjes matrices[J]. Front. Math. China, 2022, 17(5): 887-903.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0977-7
https://academic.hep.com.cn/fmc/EN/Y2022/V17/I5/887

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