Combinatorics of orthogonal polynomials of type $R_I$
Jang Soo Kim, Dennis Stanton
TL;DR
This paper develops a combinatorial framework for type R_I orthogonal polynomials, linking paths, moments, continued fractions, and determinants, with explicit examples from the Askey scheme.
Contribution
It introduces a novel combinatorial approach to analyze type R_I orthogonal polynomials, connecting various mathematical tools and providing explicit examples.
Findings
Established a combinatorial model for type R_I polynomials
Derived explicit formulas for moments and continued fractions
Connected combinatorial structures with classical orthogonal polynomials
Abstract
A combinatorial theory for type orthogonal polynomials is given. The ingredients include weighted generalized Motzkin paths, moments, continued fractions, determinants, and histories. Several explicit examples in the Askey scheme are given.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Molecular spectroscopy and chirality · Random Matrices and Applications