Baur, K, Faber, E orcid.org/0000-0003-2541-8916, Gratz, S et al. (2 more authors) (2018) Conway–Coxeter Friezes and Mutation: A Survey. In: Deines, A, Ferrero, D, Graham, E, Im, MS, Manore, C and Price, C, (eds.) Advances in the Mathematical Sciences. AWM Research Symposium, 08-09 Apr 2017, Los Angeles, USA. Springer, Cham , pp. 47-68. ISBN 978-3-319-98683-8
Abstract
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.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © The Author(s) and the Association for Women in Mathematics 2018. This is an author produced version of a conference paper published in Advances in the Mathematical Sciences. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | AR quiver; Cluster category; Cluster mutation; Cluster-tilted algebra; Frieze pattern; Caldero-Chapoton map; String module |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Jul 2018 15:49 |
Last Modified: | 01 Nov 2019 01:38 |
Status: | Published |
Publisher: | Springer, Cham |
Identification Number: | 10.1007/978-3-319-98684-5_4 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:132792 |