Stieltjes moment sequences of polynomials
Huyile Liang, Jeffrey Remmel, Sainan Zheng

TL;DR
This paper introduces the concept of Stieltjes moment sequences of polynomials, extending classical moment sequences to multivariable polynomials, and constructs a broad class of such sequences using multivariable Catalan-like numbers.
Contribution
It defines Stieltjes moment sequences of polynomials and develops multivariable analogues of Catalan-like numbers to generate new examples.
Findings
Established conditions for polynomial sequences to be Stieltjes moment sequences.
Constructed a large class of such sequences using multivariable Catalan-like numbers.
Connected total positivity of matrices to polynomial moment sequences.
Abstract
A sequence is Stieltjes moment sequence if it has the form for is a nonnegative measure on . It is known that is a Stieltjes moment sequence if and only if the matrix is totally positive, i.e., all its minors are nonnegative. We define a sequence of polynomials in to be a Stieltjes moment sequence of polynomials if the matrix is -totally positive, i.e., all its minors are polynomials in with nonnegative coefficients. The main goal of this paper is to produce a large class of Stieltjes moment sequences of polynomials by finding multivariable analogues of Catalan-like numbers as defined by Aigner.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Molecular spectroscopy and chirality · Advanced Mathematical Identities
