The Farey framework for SL₂-tilings

Research

Papers

Ian Short, Classifying SL₂-tilings, Trans. Amer. Math. Soc. 376 (2023), 1–38; arXiv:1904.11900 [math.CO].
Ian Short, Matty Van Son, Andrei Zabolotskii, Frieze patterns and Farey complexes, arXiv:2312.12953 [math.CO].
Sammy Benzaira, Ian Short, Matty van Son, Andrei Zabolotskii, Enumerating tame friezes over ℤ/nℤ, arXiv:2410.23400 [math.CO].

Featured talks

Slides for our talks at the Continued Fractions and SL₂-tilings workshop (Durham, 2024):
- Ian Short, Continued fractions, SL₂-tilings, and the Farey complex
- Matty van Son, Lifting SL₂-tilings
- Andrei Zabolotskii, Gallery of Farey graphs, and Wild SL₂-tilings

Apps

Triangulations and friezes, a demonstration of the connections between triangulated polygons, paths in the Farey graph, Conway–Coxeter friezes, and cluster variables in the cluster algebra of type A_n.