Conway–Coxeter Friezes and Mutation: A Survey

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

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

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.

Original languageEnglish
Title of host publicationAssociation for Women in Mathematics Series
Pages47-68
Number of pages22
DOIs
StatePublished - 2018

Publication series

NameAssociation for Women in Mathematics Series
Volume15
ISSN (Print)2364-5733
ISSN (Electronic)2364-5741

Bibliographical note

Publisher Copyright:
© 2018, The Author(s) and the Association for Women in Mathematics.

Keywords

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

ASJC Scopus subject areas

  • General Mathematics
  • Gender Studies

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