Dyck Paths Categories And Its Relationships With Cluster Algebras

  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},
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. 

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