{
  "abstract": "In their 1998 precursor to their celebrated paper ``Recounting the rationals,'' Calkin and Wilf listed nine open problems related to the function $b_{k,\\ell}(n)$, the number of partitions of $n$ into powers of $\\ell$ with each part appearing at most $k$ times. In this short paper, we answer five of their eight remaining open problems. As a consequence of our results, we extend and generalise results of both Carlitz and Reznick, and answer an open question of Reznick.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08109",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael Coons"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6yhm35xk6dxp1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08109",
  "fulltext_url": null,
  "id": "6yhm35xk6dxp1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08109",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08109",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6yhm35xk6dxp1.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.08109",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08109"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Calkin--Wilf problems on $\\ell$-ary partition functions",
  "title_text": "The Calkin--Wilf problems on ℓ-ary partition functions",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/6yhm35xk6dxp1",
  "venue": "arXiv",
  "versions": []
}