{
  "abstract": "In this paper, we study the combinatorial object $\\bar{b}^k_{r,s}(n)$ which counts the overcolored partition $k$-tuples wherein both even and odd parts are colored with $r$ and $s$ colors, respectively. We extend results of Chacon and Sellers for several families of $r,s$ and $k$. We also establish divisibility properties for $\\bar{b}^k_{r,s}(n)$ modulo prime $p$ and conclude with new congruences modulo powers of $2$. The techniques involved to obtain our results rely on theta function identities and modular forms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03926",
  "author_total": 2,
  "authors": [
    {
      "name": "M. P. Thejitha"
    },
    {
      "name": "S. N. Fathima"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d6xkawz2g3jez.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03926",
  "fulltext_url": null,
  "id": "d6xkawz2g3jez",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03926",
  "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": "W7208771603",
  "pdf_url": "https://arxiv.org/pdf/2609.03926",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d6xkawz2g3jez.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.03926",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03926"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Overcolored Partition $k$-tuples Restricted by Parity of the Parts",
  "title_text": "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/d6xkawz2g3jez",
  "venue": "arXiv",
  "versions": []
}