{
  "abstract": "Let $\\overline{po}_k(n)$ denote the number of $k$-colored overpartitions of $n$ into odd parts. For every odd number of colors, we establish infinite families of internal congruences modulo high powers of $2$. The proof proceeds by expressing the relevant difference generating functions as a fixed theta quotient multiplied by polynomials in an auxiliary function. Uniform lower bounds for the $2$-adic valuations of the polynomial coefficients then yield the stated internal congruences. These results generalize an internal congruence of Saikia, Sarma and Sellers (J. Ramanujan Math. Soc.~2025) on overpartition triples into odd parts.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11806",
  "author_total": 3,
  "authors": [
    {
      "name": "Manjil P. Saikia"
    },
    {
      "name": "Prabal Talukdar"
    },
    {
      "name": "Dazhao Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2qg9ke9xs0j95.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11806",
  "fulltext_url": null,
  "id": "2qg9ke9xs0j95",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11806",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7212239517",
  "pdf_url": "https://arxiv.org/pdf/2609.11806",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2qg9ke9xs0j95.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2609.11806",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11806"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Internal congruences modulo powers of 2 for $k$-colored overpartitions into odd parts",
  "title_text": "Internal congruences modulo powers of 2 for k-colored overpartitions into odd parts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/2qg9ke9xs0j95",
  "venue": "arXiv",
  "versions": []
}