Immanant positivity for Catalan-Stieltjes matrices. (English) Zbl 1509.05039
Summary: 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.
MSC:
| 05B20 | Combinatorial aspects of matrices (incidence, Hadamard, etc.) |
| 05A05 | Permutations, words, matrices |
| 05A20 | Combinatorial inequalities |
| 11B68 | Bernoulli and Euler numbers and polynomials |
| 15B48 | Positive matrices and their generalizations; cones of matrices |
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