{
  "abstract": "Koornwinder moments generalize the Askey--Wilson moments arising in the asymmetric simple exclusion process. Rains conjectured that, under the specialization $t=q$, the minimal numerators of Koornwinder moments have nonnegative integer coefficients. While the one-row case of this conjecture was previously proved by Corteel, Mandelshtam, and Williams using rhombic staircase tableaux, its dual counterpart, the one-column case, has remained open. In this paper, we derive a closed, manifestly positive combinatorial formula for the normalized numerators of the coefficients of the rescaled Askey--Wilson polynomials. This proves Rains' conjecture for one-column partitions, thereby providing the exact dual counterpart to the previous result.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24091",
  "author_total": 3,
  "authors": [
    {
      "name": "Younggwang Cho"
    },
    {
      "name": "Donghyun Kim"
    },
    {
      "name": "Jang Soo Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/27cfz71pgja62.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24091",
  "fulltext_url": null,
  "id": "27cfz71pgja62",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24091",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213995706",
  "pdf_url": "https://arxiv.org/pdf/2609.24091",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/27cfz71pgja62.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24091",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24091"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Askey--Wilson polynomials with ASEP parameters",
  "title_text": "Askey--Wilson polynomials with ASEP parameters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/27cfz71pgja62",
  "venue": "arXiv",
  "versions": []
}