{
  "abstract": "Let $A_{t,k}(n)$ denote the number of partition $k$-tuples of $n$ with $t$-cores. Using fifth-order modular equations and the Atkin $U_5$-operator, we prove the congruences $A_{5,125i+21}(25n+r)\\equiv 0 \\pmod{5^3}$ for $r\\in\\{9,14,19,24\\}$, $A_{5,125i+41}(25n+r)\\equiv 0 \\pmod{5^3}$ for $r\\in\\{19,24\\}$, and $A_{5,125i+111}(125n+r)\\equiv 0 \\pmod{5^4}$ for $r\\in\\{39,64,89,114\\}$, which were stated by Tang \\cite{tang2025iterative}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00693",
  "author_total": 1,
  "authors": [
    {
      "name": "Saikat Maity"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9zx8sg2td4f5p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00693",
  "fulltext_url": null,
  "id": "9zx8sg2td4f5p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00693",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00693",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9zx8sg2td4f5p.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00693",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00693"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On Certain Congruences for Partition $k$-Tuples with $5$-Cores",
  "title_text": "On Certain Congruences for Partition k-Tuples with $5$-Cores",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/9zx8sg2td4f5p",
  "venue": "arXiv",
  "versions": []
}