A short proof for the acyclicity of oriented exchange graphs of cluster algebras
Published: Apr 14, 2025
Last Updated: Apr 14, 2025
Authors:Shuhao Deng, Changjian Fu
Abstract
The statement in the title was proved in \cite{Cao23} by introducing dominant sets of seeds, which are analogs of torsion classes in representation theory. In this note, we observe a short proof by the existence of consistent cluster scattering diagrams.