{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "name": "Jang Soo Kim"
    },
    {
      "name": "Minho Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fjennp7k8648w.bib",
  "cited_by": 1,
  "doi": "10.37236/13718",
  "fulltext_url": null,
  "id": "fjennp7k8648w",
  "issns": [
    "1077-8926"
  ],
  "landing_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p24",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W4404573840",
  "pdf_url": "https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i4p24/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": "The Electronic Journal of Combinatorics",
  "ris": "https://research.draconitic.com/paper/fjennp7k8648w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:24Z",
      "native_id": "10.37236/13718",
      "source": "crossref",
      "url": "https://www.combinatorics.org/ojs/index.php/eljc/article/view/v33i4p24"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2607|Advanced Combinatorial Mathematics",
      "subfield": "combinatorics"
    }
  ],
  "title": "Combinatorics of Generalized Orthogonal Polynomials of Type $R_{II}$",
  "title_text": "Combinatorics of Generalized Orthogonal Polynomials of Type R_II",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:24Z",
  "url": "https://research.draconitic.com/paper/fjennp7k8648w",
  "venue": "The Electronic Journal of Combinatorics",
  "versions": []
}