Baur, K, Faber, E, Gratz, S et al. (2 more authors) (2018) Mutation of friezes. Bulletin des Sciences Mathématiques, 142. pp. 1-48. ISSN 0007-4497
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2017 Elsevier Masson SAS. All rights reserved. This is an author produced version of a paper published in Bulletin des Sciences Mathématiques. 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: | 04 Aug 2017 11:00 |
Last Modified: | 14 Sep 2018 00:38 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.bulsci.2017.09.004 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:119784 |