A survey of results linking frieze patterns to polygon triangulations, Grassmannian cluster algebras, and Grassmannian cluster categories, with focus on recent links to cluster categories.
Non-zero integral friezes
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abstract
We study non-zero integral friezes for Dynkin types $A_n$, $B_n$, $C_n$, $D_n$ and $G_2$. These differ from standard Coxeter-Conway (positive) friezes by allowing any non-zero integer to appear. In each case we show that there are either $1$, $2$ or $4$ times as many non-zero friezes as positive friezes. This is a first step for considering friezes over general rings of integers.
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math.RT 1years
2025 1verdicts
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Frieze patterns in representation theory
A survey of results linking frieze patterns to polygon triangulations, Grassmannian cluster algebras, and Grassmannian cluster categories, with focus on recent links to cluster categories.