Sl2(z)-tilings of the Torus, Coxeter-conway Friezes and Farey Triangulations

نویسندگان

  • SOPHIE MORIER-GENOUD
  • VALENTIN OVSIENKO
  • SERGE TABACHNIKOV
چکیده

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

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تاریخ انتشار 2014