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

3 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.

Funding

Acknowledgments We thank AWM for encouraging us to write this summary and giving us opportunity to continue this work. We also thank the referees for useful comments on the paper. EF, KS and GT received support from the AWM Advance grant to attend the symposium. KB was supported by the FWF grant W1230. KS was supported by NSF Postdoctoral Fellowship MSPRF-1502881. We thank AWM for encouraging us to write this summary and giving us opportunity to continue this work. We also thank the referees for useful comments on the paper. EF, KS and GT received support from the AWM Advance grant to attend the symposium. KB was supported by the FWF grant W1230. KS was supported by NSF Postdoctoral Fellowship MSPRF-1502881.

Funders	Funder number
Neurosciences Foundation
Advantage West Midlands
Austrian Science Fund/FWF	W1230
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	MSPRF-1502881

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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Conwayâ€“Coxeter Friezes and Mutation: A Survey

Abstract

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Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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