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arxiv 2504.10245 v1 pith:UCJGOBNT submitted 2025-04-14 math.RT math.RA

A short proof for the acyclicity of oriented exchange graphs of cluster algebras

Shuhao Deng , Changjian Fu This is my paper
classification math.RT math.RA
keywords clusterproofshortacyclicityalgebrasanalogscao23cite
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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.

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