Conway-Coxeter friezes and mutation: a survey

Baur, K., Faber, E., Gratz, S. , Serhiyenko, K. and Todorov, G. (2018) Conway-Coxeter friezes and mutation: a survey. In: Deines, A., Ferrero, D., Graham, E., Seong Im, M., Manore, C. and Price, C. (eds.) Advances in Mathematical Sciences. Series: Association for Women in Mathematical Sciences (15). Springer: Cham, pp. 47-68. ISBN 9783319986838 (doi:10.1007/978-3-319-98684-5_4)

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In this survey chapter, 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.

Item Type:Book Sections
Glasgow Author(s) Enlighten ID:Gratz, Dr Sira
Authors: Baur, K., Faber, E., Gratz, S., Serhiyenko, K., and Todorov, G.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Published Online:01 November 2018

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