{
  "abstract": "Let $\\NT(m,n)$ be the total number of parts in the partitions of $n$ with rank $m$, and let $\\MW(m,n)$ be the total number of ones in the partitions of $n$ with crank $m$. Using the uniform generalized-rank estimate of Liu and Zhou, we establish asymptotic formulas for $NT(m,n)$ and $\\MW(m,n)$. Put $β_n=π/\\sqrt{6n}$ and $L_n=\\log(1/β_n)$. For every fixed $A>0$, uniformly for $|m|\\le A\\sqrt n$, we prove \\begin{align*} \\NT(m,n)&=\\frac{p(n)L_n}{4}\\sech^2\\!\\left(\\frac{β_nm}{2}\\right) +O_A\\!\\bigl(p(n)\\log L_n\\bigr) \\intertext{ and} \\MW(m,n)&=\\frac{p(n)}4\\log(1+e^{-β_nm}) \\sech^2\\!\\left(\\frac{β_nm}{2}\\right) +O_A\\!\\bigl(p(n)\\sqrt{β_nL_n}\\bigr). \\end{align*}",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16024",
  "author_total": 1,
  "authors": [
    {
      "name": "Renrong Mao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3hezz3p5ckr2x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16024",
  "fulltext_url": null,
  "id": "3hezz3p5ckr2x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16024",
  "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",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7221774582",
  "pdf_url": "https://arxiv.org/pdf/2610.16024",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3hezz3p5ckr2x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.16024",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16024"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Uniform Asymptotics for Andrews-Beck Partition Statistics",
  "title_text": "Uniform Asymptotics for Andrews-Beck Partition Statistics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/3hezz3p5ckr2x",
  "venue": "arXiv",
  "versions": []
}