{
  "abstract": "The maximal entries of Dynkin friezes over the positive integers have recently been determined for all finite Dynkin types except $B_n$ and $D_n$. In this note, we explicitly construct large positive integral points on affine cluster varieties of type $B_n$ (resp. $D_n$), giving rise to friezes of types $B_n$ (resp. $D_n$) over the positive integers with largest entries $F_{n+1} F_{n+2} - 1$ (resp. $F_n F_{n+1} - 1$) where $F_k$ is the $k$-th Fibonacci number. We conjecture that these are the maximal possible entries for their respective Dynkin types.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Poly. J. Math. 4(12):1-17, 2026",
  "arxiv": "2606.02870",
  "author_total": 1,
  "authors": [
    {
      "name": "Robin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/28196gpj62t98.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.02870",
  "fulltext_url": null,
  "id": "28196gpj62t98",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.02870",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.02870",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/28196gpj62t98.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2606.02870",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.02870"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On maximal Dynkin friezes",
  "title_text": "On maximal Dynkin friezes",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/28196gpj62t98",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.69763/polyjmath.4.12",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}