Conwayâ€“Coxeter Friezes and Mutation: A Survey

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

doi:10.1007/978-3-319-98684-5_4

Conwayâ€“Coxeter Friezes and Mutation: A Survey

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

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

In this survey chapter, we explain the intricate links between Conwayâ€“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 language	English
Title of host publication	Association for Women in Mathematics Series
Pages	47-68
Number of pages	22
DOIs	https://doi.org/10.1007/978-3-319-98684-5_4
State	Published - 2018

Publication series

Name	Association for Women in Mathematics Series
Volume	15
ISSN (Print)	2364-5733
ISSN (Electronic)	2364-5741

Bibliographical note

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

Keywords

AR quiver
Calderoâ€“Chapoton map
Cluster category
Cluster mutation
Cluster-tilted algebra
Frieze pattern
String module

ASJC Scopus subject areas

General Mathematics
Gender Studies

Access to Document

10.1007/978-3-319-98684-5_4

Cite this

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AU - Todorov, Gordana

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Conwayâ€“Coxeter Friezes and Mutation: A Survey

Abstract

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Keywords

ASJC Scopus subject areas

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