{
  "abstract": "While people have studied $m$-ary partitions of an integer $n$ and studied conjugation of partitions of $n$, these topics are rarely mixed because the $m$-ary property is almost always lost after conjugation. In a previous work, Flowers and Lockard investigated $m$-ary partitions of $n$ whose conjugates were also $m$-ary. We generalize that previous work by studying $m$-ary partitions whose conjugates are $q$-ary, where $m$ and $q$ may be distinct. We provide a family of operators on these partitions that can be used to generate all such partitions uniquely and associate a unique polynomial with each partition based on the sequence of operators used to generate it. Using the generating operators and modular arithmetic we explore many examples and families of $m$-ary partitions whose conjugates are $q$-ary.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Journal of Algebra Combinatorics Discrete Structures and Applications (2026), 13(3), 385-407",
  "arxiv": "2609.08799",
  "author_total": 3,
  "authors": [
    {
      "name": "Geoffrey D. Dietz"
    },
    {
      "name": "Timothy B. Flowers"
    },
    {
      "name": "Shannon R. Lockard"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/028sapy6br0ba.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08799",
  "fulltext_url": null,
  "id": "028sapy6br0ba",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08799",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.08799",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/028sapy6br0ba.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.08799",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08799"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A study of $m$-ary partitions whose conjugates are $q$-ary",
  "title_text": "A study of m-ary partitions whose conjugates are q-ary",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/028sapy6br0ba",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.13069/jacodesmath.v13i3.393",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}