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PreprintarXiv licencearXiv

Triangulated polygons and Y-frieze patterns

  • Hin Chung Henry Tsang
  • Jon Wilson
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Abstract

In the spirit of Conway and Coxeter, we classify all Y-frieze patterns of type An. In particular, we settle a conjecture made by de Saint Germain that all such Y-frieze patterns arise from Conway-Coxeter frieze patterns. Moreover, our approach naturally leads to the enumeration of these Y-frieze patterns in terms of Fuss-Catalan numbers.

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Cite

BibTeXRIS
BibTeX
@misc{tsang2026triangulated,
  title = {{Triangulated polygons and Y-frieze patterns}},
  author = {Hin Chung Henry Tsang and Jon Wilson},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29655},
  eprint = {2608.29655},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29655},
}
RIS
TY  - UNPB
TI  - Triangulated polygons and Y-frieze patterns
AU  - Hin Chung Henry Tsang
AU  - Jon Wilson
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.29655
UR  - https://arxiv.org/abs/2608.29655
AB  - In the spirit of Conway and Coxeter, we classify all Y-frieze patterns of type A_n. In particular, we settle a conjecture made by de Saint Germain that all such Y-frieze patterns arise from Conway-Coxeter frieze patterns. Moreover, our approach naturally leads to the enumeration of these Y-frieze patterns in terms of Fuss-Catalan numbers.
ER  -