{
  "abstract": "We study two Riordan arrays associated with the Motzkin-prefix sequence (\\href{https://oeis.org/A005773}{OEIS A005773}). By connecting their production matrices through a simple boundary factorization, we obtain a period-three transformation on Motzkin endpoint distributions and exact formulas for paths by final height modulo~$3$. In addition, a unified factorization for the shifted Hankel matrices leads directly to explicit closed forms for the third and fourth Hankel determinants, $Δ_n^{(3)}$ and~$Δ_n^{(4)}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00775",
  "author_total": 2,
  "authors": [
    {
      "name": "Daniel Yaqubi"
    },
    {
      "name": "Madjid Mirzavaziri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b052yhyhr7v6d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00775",
  "fulltext_url": null,
  "id": "b052yhyhr7v6d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00775",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7216282464",
  "pdf_url": "https://arxiv.org/pdf/2610.00775",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b052yhyhr7v6d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.00775",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00775"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Riordan Arrays and Shifted Hankel Determinants of OEIS A005773",
  "title_text": "Riordan Arrays and Shifted Hankel Determinants of OEIS A005773",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/b052yhyhr7v6d",
  "venue": "arXiv",
  "versions": []
}