Abstract
It is known that any infinite periodic frieze comes from a triangulation of an annulus by Theorem 4.6 of [K. Baur, M. J. Parsons and M. Tschabold, Infinite friezes, European J. Combin. 54 (2016) 220-237]. In this paper, we show that each infinite periodic frieze determines a triangulation of an annulus in essentially a unique way. Since each triangulation of an annulus determines a pair of friezes, we study such pairs and show how they determine each other. We study associated module categories and determine the growth coefficient of the pair of friezes in terms of modules as well as their quiddity sequences.
| Original language | English |
|---|---|
| Article number | 2450207 |
| Pages (from-to) | 220-237 |
| Number of pages | 18 |
| Journal | Journal of Algebra and its Applications |
| Volume | 23 |
| Issue number | 12 |
| Early online date | 27 Jun 2023 |
| DOIs | |
| Publication status | Published - Oct 2024 |
Bibliographical note
Publisher Copyright:© 2024 World Scientific Publishing Company.
Keywords
- annulus
- cluster categories
- Conway-Coxeter friezes
- frieze patterns
- growth coefficients
- infinite friezes
- triangulation