Higher frieze patterns

Abstract

Frieze patterns have an interesting combinatorial structure, which has proven very useful in the study of cluster algebras. We introduce $(k,n)$-frieze patterns, a natural generalisation of the classical notion. A generalisation of the bijective correspondence between frieze patterns of width $n$ and clusters of Plücker coordinates in the cluster structure of the Grassmannian $\mathrm{Gr}(2,n+3)$ is obtained.

Updated to include a connection to $\mathrm{SL}_k}$-friezes

Cited by in corpus (2)

• Tropical friezes and the index in higher homological algebra
• Quiddity sequences for ${\mathrm{SL}}_3$-frieze patterns