Dyck path categories and its relationships with cluster algebras
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Published:2022-10-26
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Volume:
Page:
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ISSN:0219-4988
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Container-title:Journal of Algebra and Its Applications
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language:en
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Short-container-title:J. Algebra Appl.
Author:
Cañadas Agustín Moreno1,
Rios Gabriel Bravo1
Affiliation:
1. Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá-Colombia
Abstract
Dyck path categories are introduced as a combinatorial model of the category of representations of quivers of Dynkin-type [Formula: see text]. 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 [Formula: see text] in terms of Dyck paths.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory