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      \(SL_2(\mathbb{Z})\)-tilings of the torus, Coxeter-Conway friezes and Farey triangulations

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          Abstract

          The notion of \(SL_2\)-tiling is a generalization of that of classical Coxeter-Conway frieze pattern. We classify doubly antiperiodic \(SL_2\)-tilings that contain a rectangular domain of positive integers. Every such \(SL_2\)-tiling corresponds to a pair of frieze patterns and a unimodular \(2\times2\)-matrix with positive integer coefficients. We relate this notion to triangulated \(n\)-gons in the Farey graph.

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          Journal
          22 February 2014
          2014-04-16
          Article
          1402.5536
          289918be-f1cc-4a8b-87c3-80ad34035908

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          5 figures
          math.CO math.NT

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