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

Producción científica: Chapter › revisión exhaustiva

2 Citas (Scopus)

Resumen

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.

Idioma original	English
Título de la publicación alojada	Association for Women in Mathematics Series
Páginas	47-68
Número de páginas	22
DOI	https://doi.org/10.1007/978-3-319-98684-5_4
Estado	Published - 2018

Serie de la publicación

Nombre	Association for Women in Mathematics Series
Volumen	15
ISSN (versión impresa)	2364-5733
ISSN (versión digital)	2364-5741

Nota bibliográfica

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

Financiación

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.

Financiadores	Número del financiador
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

ASJC Scopus subject areas

General Mathematics
Gender Studies

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Conwayâ€“Coxeter Friezes and Mutation: A Survey

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Nota bibliográfica

Financiación

ASJC Scopus subject areas

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