{
  "abstract": "In a famous paper of Andrews, he defined and studied the smallest parts function $\\operatorname{spt}(n)$. He showed that it satisfies the three Ramanujan-type congruences: \\[ \\operatorname{spt}(5n+4)\\equiv0\\pmod5,\\qquad \\operatorname{spt}(7n+5)\\equiv0\\pmod7,\\qquad \\operatorname{spt}(13n+6)\\equiv0\\pmod{13}. \\] In a recent preprint, the author showed that these are the only \"canonical'' congruences. Here, we complete the classification of Ramanujan-type congruences for $\\operatorname{spt}$, showing that if $\\operatorname{spt}(\\ell n+b)\\equiv0\\pmod\\ell$ for all $n\\geq0$, where $\\ell\\geq5$ is prime, then $(\\ell,b)\\in\\{(5,4),(7,5),(13,6)\\}.$ That is, Andrews' congruences are the only Ramanujan-type congruences for $\\operatorname{spt}(n)$. These results have been verified in Lean by AxiomProver.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04178",
  "author_total": 1,
  "authors": [
    {
      "name": "Larry Rolen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a6batb3wekkd8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04178",
  "fulltext_url": null,
  "id": "a6batb3wekkd8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04178",
  "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.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04178",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a6batb3wekkd8.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04178",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04178"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Ramanujan-type congruences for the smallest parts function",
  "title_text": "Ramanujan-type congruences for the smallest parts function",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:29Z",
  "url": "https://research.draconitic.com/paper/a6batb3wekkd8",
  "venue": "arXiv",
  "versions": []
}