{
  "abstract": "In recent work, Hirschhorn and the second author defined $a_k(n)$ to be the number of partitions of $n$ wherein the even parts come in only one color, while the odd parts may be ``colored'' with one of $k$ colors for fixed $k\\geq 1$. This function generalizes the classical partition function and has been of significant interest because it satisfies a number of congruences. Although prior work studying $a_k(n)$ has resulted in congruences in arithmetic progressions in a somewhat ad hoc manner, this work gives a uniform framework for studying congruences modulo 3. This allows us to prove an infinite family of infinite families of non-nested congruences modulo 3.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19440",
  "author_total": 2,
  "authors": [
    {
      "name": "Marie Jameson"
    },
    {
      "name": "James A. Sellers"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/62ynne03asnwv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19440",
  "fulltext_url": null,
  "id": "62ynne03asnwv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19440",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7213595896",
  "pdf_url": "https://arxiv.org/pdf/2609.19440",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/62ynne03asnwv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.19440",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19440"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A uniform proof approach for congruences modulo 3 for partitions with $k$-colored odd parts",
  "title_text": "A uniform proof approach for congruences modulo 3 for partitions with k-colored odd parts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/62ynne03asnwv",
  "venue": "arXiv",
  "versions": []
}