2021
DOI: 10.48550/arxiv.2106.12816
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Immanant Positivity for Catalan-Stieltjes Matrices

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, Schröder polynomials and Narayana polynomials.

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Cited by 1 publication
(4 citation statements)
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“…We have verified the immanant positivity of all square submatrices of H n for n ≤ 6 by Sage [21]. Note that, our method in [13] does not apply to H directly, since there exist some arcs weighted by −1 in our planar network for H.…”
Section: A Conjecture On Immanant Positivitymentioning
confidence: 84%
See 3 more Smart Citations
“…We have verified the immanant positivity of all square submatrices of H n for n ≤ 6 by Sage [21]. Note that, our method in [13] does not apply to H directly, since there exist some arcs weighted by −1 in our planar network for H.…”
Section: A Conjecture On Immanant Positivitymentioning
confidence: 84%
“…When λ = (1 n ), the immanant Imm λ M specializes to det[M]. In [13] we proved the immanant positivity for a large family of Catalan-Stieltjes matrices and their associated Hankel matrices. This motivates us to study the the immanant positivity for the Hankel matrix H defined as in (1.1).…”
Section: A Conjecture On Immanant Positivitymentioning
confidence: 90%
See 2 more Smart Citations