Conway-Coxeter friezes and mutation: a survey
Rings and Algebras
2018-06-19 v1 Combinatorics
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 in the sense of Caldero and Chapoton.
Keywords
Cite
@article{arxiv.1806.06441,
title = {Conway-Coxeter friezes and mutation: a survey},
author = {Karin Baur and Eleonore Faber and Sira Gratz and Khrystyna Serhiyenko and Gordana Todorov},
journal= {arXiv preprint arXiv:1806.06441},
year = {2018}
}
Comments
18 pages, 10 figures; Version submitted to the proceedings of the 2017 AWM Research Symposium