{
  "abstract": "In this paper, we classify the Conway symbols of the Euclidean symmetry groups of frieze patterns of Dynkin types $A_n$, $B_n$, $C_n$, $D_n$, $F_4$ and $G_2$. First, we show that the Conway symbol of a Conway--Coxeter frieze is determined by the bilateral and the central symmetry of the underlying triangulation. Secondly, we show that a frieze pattern of non-simply-laced type has the symbol ${*}\\infty\\infty$ or $\\infty\\infty$ according as its first interior row is palindromic or not, with the single exception of type $C_3$, which realises four symbols. Thirdly, we show that the same dichotomy holds for type $D_n$ with $n \\ge 5$, the symbol being read off the tagged triangulation of the once-punctured polygon attached to the frieze together with the value on its puncture edges, and that type $D_4$ realises five symbols.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14948",
  "author_total": 2,
  "authors": [
    {
      "name": "Kengo Miyamoto"
    },
    {
      "name": "Ryuhei Suzuki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0yz25wcpp7qjs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14948",
  "fulltext_url": null,
  "id": "0yz25wcpp7qjs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14948",
  "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"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7213237079",
  "pdf_url": "https://arxiv.org/pdf/2609.14948",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0yz25wcpp7qjs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14948",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14948"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Conway Symbols of Frieze Patterns of Dynkin Types",
  "title_text": "Conway Symbols of Frieze Patterns of Dynkin Types",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/0yz25wcpp7qjs",
  "venue": "arXiv",
  "versions": []
}