{
  "abstract": "Let $R_N(m)$ count unordered partitions of $m$ into reduced positive fractions whose numerators and denominators are at most $N$, excluding integer parts. Uniformly for $ρ$ in compact positive intervals, $\\log R_N(\\lfloorρN\\rfloor)=\\sqrt{2ρ}\\,N^{3/2}-κ(ρ)N^{3/2}/\\log N+o(N^{3/2}/\\log N)$. The positive, continuously differentiable function $κ$ is an explicit sum of lattice-distance integrals, with $κ(1)\\approx 0.00264713$. For a uniform partition of $n$, all but $o_{\\mathbb{P}}(n/\\log n)$ prime-denominator blocks in $(n/2,n]$ have total 2 or 3, according to whether $p/n$ lies below or above an explicit threshold near 0.7522. For fixed $N$, we give the Ehrhart numerator and determine how its poles control quasipolynomial coefficients. Its residue distribution is asymmetric for $N\\ge 4$, but agrees with an independent model in every moment below order $\\lceil N/2\\rceil$. We identify the first discrepancy and prove a Gaussian limit. We also obtain joint denominator and size laws under two sampling rules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18945",
  "author_total": 1,
  "authors": [
    {
      "name": "K. Srinivasa Raghava"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ajbgfen8bjbv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18945",
  "fulltext_url": null,
  "id": "3ajbgfen8bjbv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18945",
  "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"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213509015",
  "pdf_url": "https://arxiv.org/pdf/2609.18945",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ajbgfen8bjbv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18945",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18945"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Arithmetic Constraints and Limit Laws for Diagonal Rational Partitions",
  "title_text": "Arithmetic Constraints and Limit Laws for Diagonal Rational Partitions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/3ajbgfen8bjbv",
  "venue": "arXiv",
  "versions": []
}