\(SL_k\)-tilings of the plane

zbMath1236.13018arXiv1002.1089MaRDI QIDQ716402

François Bergeron, Christophe Reutenauer

Publication date: 28 April 2011

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.1089

zbMATH Keywords

Laurent phenomenonT-systemsfrieze patterns\(SL_2\)-tilingsinfinite arrays

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Combinatorial aspects of representation theory (05E10) Determinants, permanents, traces, other special matrix functions (15A15) Matrices, determinants in number theory (11C20) Cluster algebras (13F60)

Related Items (17)

All \(\operatorname{SL}_{2}\)-tilings come from infinite triangulations ⋮ Combinatorics of congruence subgroups of the modular group. II ⋮ Classifying 𝑆𝐿₂-tilings ⋮ Farey boat: continued fractions and triangulations, modular group and polygon dissections ⋮ \(T\)-systems, networks and dimers ⋮ Categorification of a frieze pattern determinant ⋮ Commuting difference operators and the combinatorial Gale transform ⋮ Mutating seeds: types \(\mathbb{A}\) and \(\tilde{\mathbb{A}}\) ⋮ Infinite friezes of cluster algebras from surfaces ⋮ Some elements of combinatorics of \(\mathrm{SL}_2 (\mathbb{Z})\) matrices ⋮ Arithmetics of 2-friezes ⋮ 2-frieze patterns and the cluster structure of the space of polygons ⋮ Symplectic frieze patterns ⋮ Counting Coxeter's friezes over a finite field via moduli spaces ⋮ Partitions of unity in \(\mathrm{SL}(2,\mathbb Z)\), negative continued fractions, and dissections of polygons ⋮ Cluster algebraic interpretation of infinite friezes ⋮ Linear difference equations, frieze patterns, and the combinatorial Gale transform

Cites Work

• Unnamed Item
• Friezes
• The Laurent phenomenon
• The solution of the A\(_{r}\) T-system for arbitrary boundary
• \(Q\)-systems as cluster algebras. II: Cartan matrix of finite type and the polynomial property
• Binomial determinants, paths, and hook length formulae
• Positivity of the \(T\)-system cluster algebra
• Generalized frieze patterns
• FUNCTIONAL RELATIONS IN SOLVABLE LATTICE MODELS I: FUNCTIONAL RELATIONS AND REPRESENTATION THEORY
• Restricted solid-on-solid models connected with simply laced algebras and conformal field theory
• Triangulated polygons and frieze patterns
• Frieze patterns

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