Mutation of friezes

Baur, K., Faber, E., Gratz, S. , Serhiyenko, K. and Todorov, G. (2018) Mutation of friezes. Bulletin des Sciences Mathématiques, 142, pp. 1-48. (doi:10.1016/j.bulsci.2017.09.004)

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Abstract

We study mutations of Conway-Coxeter friezes which are compatible with mutations of cluster-tilting objects in the associated cluster category of Dynkin type A. 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. We observe how the frieze can be divided into four distinct regions, relative to the entry at which we want to mutate, where any two entries in the same region obey the same mutation rule. 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:Articles
Status:Published
Refereed:Yes
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
Journal Name:Bulletin des Sciences Mathématiques
Publisher:Elsevier
ISSN:0007-4497
ISSN (Online):1952-4773
Published Online:14 September 2017
Copyright Holders:Copyright © 2017 Elsevier Masson SAS
First Published:First published in Bulletin des Sciences Mathematiques 142: 1-48
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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