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arXiv · 1806.06441

Conway-Coxeter friezes and mutation: a survey

Karin Baur·Eleonore Faber·Sira Gratz·Khrystyna Serhiyenko·Gordana Todorov
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Abstract

In this survey article we explain the intricate links between Conway-Coxeter friezes and cluster combinatorics. More precisely, we provide a formula, relying solely on the shape of the frieze, describing how each individual entry in the frieze changes under cluster mutation. Moreover, we provide a combinatorial formula for the number of submodules of a string module, and with that a simple way to compute the frieze associated to a fixed cluster tilting object in a cluster category of Dynkin type $A$ in the sense of Caldero and Chapoton.

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Karin Baur, Eleonore Faber, Sira Gratz, Khrystyna Serhiyenko, Gordana Todorov. 2018-06-17. Conway-Coxeter friezes and mutation: a survey. https://arxiv.org/abs/1806.06441

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