Immanant positivity for Catalan-Stieltjes matrices

Immanant positivity for Catalan-Stieltjes matrices

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 applic...

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Veröffentlicht in:Frontiers of Mathematics 2022-10, Vol.17 (5), p.887-903
Hauptverfasser: Li, Ethan Y. H., Li, Grace M. X., Yang, Arthur L. B., Zhang, Candice X. T.
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorial analysis
Hankel matrices
Mathematics
Mathematics and Statistics
Polynomials
Research Article
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Zusammenfassung: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.
ISSN:2731-8648
1673-3452
2731-8656
1673-3576
DOI:10.1007/s11464-021-0977-7