Mutation of friezes

Karin Baur, Eleonore Faber, Sira Gratz, Khrystyna Serhiyenko, Gordana Todorov

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

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.

Original languageEnglish
Pages (from-to)1-48
Number of pages48
JournalBulletin des Sciences Mathematiques
Volume142
DOIs
StatePublished - Feb 2018

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Masson SAS

Keywords

  • AR-quiver
  • Caldero–Chapoton map
  • Cluster category
  • Cluster mutation
  • Cluster-tilted algebra
  • Frieze pattern
  • String module

ASJC Scopus subject areas

  • General Mathematics

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