\(\mathrm{SL}_2(\mathbb{Z})\)-tilings of the torus, Coxeter-Conway friezes and Farey triangulations

DOI10.4171/LEM/61-1/2-4zbMath1331.05022arXiv1402.5536OpenAlexW2963413658MaRDI QIDQ5963020

Sophie Morier-Genoud, Sergei Tabachnikov, Valentin Ovsienko

Publication date: 25 February 2016

Published in: L'Enseignement Mathématique. 2e Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.5536

zbMATH Keywords

modular group\(\mathrm{SL}_2\)-tilingFarey graphfrieze pattern

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Recurrences (11B37) Combinatorial aspects of tessellation and tiling problems (05B45) Farey sequences; the sequences (1^k, 2^k, dots) (11B57) Cluster algebras (13F60)

Related Items (10)

All \(\operatorname{SL}_{2}\)-tilings come from infinite triangulations ⋮ Rotundus: triangulations, Chebyshev polynomials, and Pfaffians ⋮ Classifying 𝑆𝐿₂-tilings ⋮ Coxeter's frieze patterns at the crossroads of algebra, geometry and combinatorics ⋮ A note on friezes of type \(\varLambda_p\) ⋮ Farey boat: continued fractions and triangulations, modular group and polygon dissections ⋮ Commuting difference operators and the combinatorial Gale transform ⋮ Pappus Theorem, Schwartz Representations and Anosov Representations ⋮ Counting Subwords Occurrences in Base-b Expansions ⋮ Partitions of unity in \(\mathrm{SL}(2,\mathbb Z)\), negative continued fractions, and dissections of polygons

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