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PreprintCC BY-NC-ND 4.0arXiv

On the frieze patterns by Conway and Coxeter

  • Anna Felikson
  • Pavel Tumarkin
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Abstract

The story of frieze patterns started in 1970s with a paper by Coxeter and two short papers by Conway and Coxeter, one listing questions and the other providing brief answers. During the first three decades it was followed by only a handful of papers observing some further properties of the same objects. Then Propp (2005) and Caldero and Chapoton (2006) established connections between frieze patterns and the recent theory of cluster algebras introduced by Fomin and Zelevinsky in early 2000s. Since then the theory of frieze patterns exploded with new results, and frieze patterns found a wide spectrum of connections in various domains of mathematics, including combinatorics, geometry, representation theory and integrable systems. The literature on frieze patterns grew vastly and continues to expand. In this note we give a brief overview of some of the directions emerging from the papers by Conway and Coxeter and single out core ideas which were later replayed in different contexts.

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Cite

BibTeXRIS
BibTeX
@misc{felikson2026frieze,
  title = {{On the frieze patterns by Conway and Coxeter}},
  author = {Anna Felikson and Pavel Tumarkin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35968},
  eprint = {2610.35968},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35968},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On the frieze patterns by Conway and Coxeter
AU  - Anna Felikson
AU  - Pavel Tumarkin
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.35968
UR  - https://arxiv.org/abs/2610.35968
AB  - The story of frieze patterns started in 1970s with a paper by Coxeter and two short papers by Conway and Coxeter, one listing questions and the other providing brief answers. During the first three decades it was followed by only a handful of papers observing some further properties of the same objects. Then Propp (2005) and Caldero and Chapoton (2006) established connections between frieze patterns and the recent theory of cluster algebras introduced by Fomin and Zelevinsky in early 2000s. Since then the theory of frieze patterns exploded with new results, and frieze patterns found a wide spectrum of connections in various domains of mathematics, including combinatorics, geometry, representation theory and integrable systems. The literature on frieze patterns grew vastly and continues to expand. In this note we give a brief overview of some of the directions emerging from the papers by Conway and Coxeter and single out core ideas which were later replayed in different contexts.
ER  -