{
  "abstract": "We prove the following conjecture of Zhang (arXiv:2604.10779, Conjecture 6.1): for $n \\geq 0$, the number of $2$-stack-sortable permutations of $\\{0,1,\\dots,n\\}$ ending in $0$ is the $n$th Motzkin number. By Zhang's result, there is a bijection between $2$-stack-sortable permutations ending in their least element and standard composition tableaux of width at most $2$. We then show bijectively that there are an equal number of these and standard Young tableaux of width at most $3$, which are known to be counted by the Motzkin numbers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02756",
  "author_total": 2,
  "authors": [
    {
      "name": "Ryota Inagaki"
    },
    {
      "name": "Michael Luo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ah8md7fpn7422.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02756",
  "fulltext_url": null,
  "id": "ah8md7fpn7422",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02756",
  "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": "W7220377663",
  "pdf_url": "https://arxiv.org/pdf/2610.02756",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ah8md7fpn7422.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02756",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02756"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Motzkin Numbers Count 2-Stack-Sortable Permutations Ending in Their Least Entry",
  "title_text": "Motzkin Numbers Count 2-Stack-Sortable Permutations Ending in Their Least Entry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/ah8md7fpn7422",
  "venue": "arXiv",
  "versions": []
}