Abstract
Hexagonal circle patterns are introduced, and a subclass thereof is studied in detail. It is characterized by the following property: for every circle the multi-ratio of its six intersection points with neighboring circles is equal to −1. The relation of such patterns with an integrable system on the regular triangular lattice is established. A kind of a Bäcklund transformation for circle patterns is studied. Further, a class of isomonodromic solutions of the aforementioned integrable system is introduced, including circle patterns analogs to the analytic functions zα and logz.
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