{
  "abstract": "In recent work, authors defined $\\bar{b}^k_{r,s}(n)$ to be the number of overcolored partition $k$-tuples wherein both even and odd parts are colored with $r$ and $s$ colors, respectively. This function generalizes the overcubic partition $k$-tuples studied by Chacon and Sellers. The present work gives a uniform framework for studying congruences for $\\bar{b}^k_{r,s}(n)$ modulo odd primes. For example, we prove that, for $n\\ge 1$, \\begin{align*} \\bar{b}_{4,2}^4(5n)\\equiv 0\\pmod{5}. \\end{align*}",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32614",
  "author_total": 2,
  "authors": [
    {
      "name": "M. P. Thejitha"
    },
    {
      "name": "S. N. Fathima"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/89pkdf8088bah.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32614",
  "fulltext_url": null,
  "id": "89pkdf8088bah",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32614",
  "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.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7214727565",
  "pdf_url": "https://arxiv.org/pdf/2609.32614",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/89pkdf8088bah.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32614",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32614"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Congruences for Overcolored Partition $k$-tuples Restricted by Parity of the Parts",
  "title_text": "Congruences for Overcolored Partition k-tuples Restricted by Parity of the Parts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/89pkdf8088bah",
  "venue": "arXiv",
  "versions": []
}