Conway-Coxeter friezes and mutation: a survey

Autor:	Baur, Karin, Faber, Eleonore, Gratz, Sira, Serhiyenko, Khrystyna, Todorov, Gordana
Rok vydání:	2018
Předmět:	Mathematics - Rings and Algebras Mathematics - Combinatorics 16G20 15E15 15E10 18D99
Druh dokumentu:	Working Paper
Popis:	In this survey article 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. Comment: 18 pages, 10 figures; Version submitted to the proceedings of the 2017 AWM Research Symposium
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1806.06441 Zobrazit plný text záznamu View this record from Arxiv