# Dyck Paths Categories And Its Relationships With Cluster Algebras

@article{Caadas2022DyckPC, title={Dyck Paths Categories And Its Relationships With Cluster Algebras}, author={Agust{\'i}n Moreno Ca{\~n}adas and Gabriel Bravo R'ios}, journal={Journal of Algebra and Its Applications}, year={2022} }

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.

## One Citation

### Coxeter’s Frieze Patterns Arising from Dyck Paths

- Mathematics
- 2021

Frieze patterns are defined by objects of a category of Dyck paths, to do that, it is introduced the notion of diamond of Dynkin type $${\mathbb {A}}_{n}$$
. Such diamonds constitute a tool to build…

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