{
  "abstract": "Recently, the study of the number of $k$-colored generalized Frobenius partitions, denoted by $cϕ_k(n)$, has witnessed renewed interest. In this paper, we investigate congruence properties of $cϕ_{16}(n)$ and $cϕ_{18}(n)$. Our main result is a proof of the conjecture of Cui, Gu, and Tang \\cite{CGT25} that, for all $n\\ge0$, $cϕ_{18}(3n+2)\\equiv0\\pmod{2187}$. The proof uses a $(p,k)$-parametrization together with $q$-series identities and dissections. We also establish congruences for $cϕ_{16}(n)$ modulo $1024$ and $2048$, and for $cϕ_{18}(n)$ modulo $8$ and $81$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.05302",
  "author_total": 3,
  "authors": [
    {
      "name": "Hirakjyoti Das"
    },
    {
      "name": "Hemjyoti Nath"
    },
    {
      "name": "Abhishek Sarma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/23t91azp0zedp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.05302",
  "fulltext_url": null,
  "id": "23t91azp0zedp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.05302",
  "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": "W7211884956",
  "pdf_url": "https://arxiv.org/pdf/2609.05302",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/23t91azp0zedp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.05302",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.05302"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Proof of a Conjecture of Cui, Gu and Tang on 18-Colored Generalized Frobenius Partitions",
  "title_text": "Proof of a Conjecture of Cui, Gu and Tang on 18-Colored Generalized Frobenius Partitions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/23t91azp0zedp",
  "venue": "arXiv",
  "versions": []
}