Dyck Paths Categories And Its Relationships With Cluster Algebras
Representation Theory
2021-02-08 v1 Rings and Algebras
Abstract
Dyck paths categories are introduced as a combinatorial model of the category of representations of quivers of Dynkin type An. In particular, it is proved that there is a bijection between some Dyck paths and perfect matchings of some snake graphs. The approach allows us to give formulas for cluster variables in cluster algebras of Dynkin type An in terms of Dyck paths.
Keywords
Cite
@article{arxiv.2102.02974,
title = {Dyck Paths Categories And Its Relationships With Cluster Algebras},
author = {Agustín Moreno Cañadas and Gabriel Bravo Ríos},
journal= {arXiv preprint arXiv:2102.02974},
year = {2021}
}