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

Abstract

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

18 pages

References in corpus (3)

• Total positivity, Grassmannians, and networks
• Internally Calabi-Yau algebras and cluster-tilting objects
• Higher frieze patterns