The Electronic Journal of Combinatorics· 2026Q1
Combinatorics of Generalized Orthogonal Polynomials of Type $R_{II}$
- 1citations
- Q1SCImago
- 2026year
Short summary
This paper establishes a combinatorial interpretation for generalized orthogonal polynomials of type $R_{II}$, extending previous work and unifying models for various polynomial types.
AI-generated from the title and abstract; the full text is not read.
Key points
- Introduces a combinatorial interpretation for orthogonal polynomials of type $R_{II}$.
- Generalizes type $R_{II}$ orthogonal polynomials by relaxing specific conditions.
- Proves a master theorem unifying combinatorial models for generalized moments of multiple orthogonal polynomial types.
- Offers a combinatorial interpretation for generalized dual coefficients.
AI-generated from the title and abstract; the full text is not read.
Abstract
In 1995, Ismail and Masson introduced orthogonal polynomials of types $R_I$ and $R_{II}$, which are defined by specific three-term recurrence relations with additional conditions. Recently, Kim and Stanton found a combinatorial interpretation for the moments of orthogonal polynomials of type $R_I$ in the spirit of the combinatorial theory of orthogonal polynomials due to Flajolet and Viennot. In this paper, we push this combinatorial model further to orthogonal polynomials of type $R_{II}$. Moreover, we generalize orthogonal polynomials of type $R_{II}$ by relaxing some of their conditions. Under a basis condition, we then prove a master theorem that generalizes combinatorial models for generalized moments of various types of orthogonal polynomials; ordinary orthogonal polynomials, Laurent biorthogonal polynomials, and orthogonal polynomials of types $R_I$ and $R_{II}$. We also give a combinatorial interpretation of the generalized dual coefficients.
The authors' abstract, as published at the source. The Electronic Journal of Combinatorics, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics