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 language | English |
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Title of host publication | Association for Women in Mathematics Series |
Pages | 47-68 |
Number of pages | 22 |
DOIs | |
State | Published - 2018 |
Publication series
Name | Association for Women in Mathematics Series |
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Volume | 15 |
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