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The notion of a $(k,n)$-frieze pattern was introduced by the author as ageneralisation of the classical frieze patterns. In this article we describeconnections between classes of $(3,n)$-frieze patterns and classes of$\mathrm{SL}_3$-frieze patterns. We introduce the idea of a superimposedtriangulation and clarify how superimposed triangulations may be used tounderstand quiddity sequences for $\mathrm{SL}_3$-frieze patterns.

Quiddity sequences for $\mathrm{SL}_3$-frieze patterns