{
  "abstract": "Let $a_k(n)$ denote the number of partitions of $n$ in which even parts occur in one color and odd parts may occur in $k$ colors. We prove infinite families of congruences modulo powers of $7$ for $a_k(n)$ when $k \\in \\{4,5,7\\}$. For each positive integer $α$, let $λ_{k,α}$ be the least nonnegative solution of $24λ_{k,α}\\equiv-(k-2)\\pmod{7^α}$. Then, we show that \\[ a_k(7^αn+λ_{k,α}) \\equiv 0\\pmod{7^{\\lfloor(α+1)/2\\rfloor}} \\] for every nonnegative integer $n$. These results extend congruences modulo $7$ of Hirschhorn and Sellers (2026) and complement Chen's (2025) congruences for the reciprocal crank parity function $a_3(n)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35292",
  "author_total": 3,
  "authors": [
    {
      "name": "Saikat Maity"
    },
    {
      "name": "Manjil P. Saikia"
    },
    {
      "name": "Prabal Talukdar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ekff0neywe9jx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35292",
  "fulltext_url": null,
  "id": "ekff0neywe9jx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35292",
  "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",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7223910130",
  "pdf_url": "https://arxiv.org/pdf/2610.35292",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ekff0neywe9jx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35292",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35292"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Congruences modulo powers of $7$ for partitions with colored odd parts",
  "title_text": "Congruences modulo powers of $7$ for partitions with colored odd parts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/ekff0neywe9jx",
  "venue": "arXiv",
  "versions": []
}