SL₂(\ℤ)-tilings of the torus, Coxeter-Conway friezes and\n Farey triangulations

2014/02/22 by Sophie Morier-Genoud, Morier-Genoud, Sophie, Valentin Ovsienko +3
Materials Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Supramolecular Self-Assembly in Materials

paper · pdf · doi:10.48550/arxiv.1402.5536

openalex publication_date 2014/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The notion of SL₂-tiling is a generalization of that of classical\nCoxeter-Conway frieze pattern. We classify doubly antiperiodic SL₂-tilings\nthat contain a rectangular domain of positive integers. Every such\nSL₂-tiling corresponds to a pair of frieze patterns and a unimodular\n2\×2-matrix with positive integer coefficients. We relate this notion to\ntriangulated n-gons in the Farey graph.\n

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