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arXiv · 2504.10245

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

Shuhao Deng·Changjian Fu
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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.

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Shuhao Deng, Changjian Fu. 2025-04-14. A short proof for the acyclicity of oriented exchange graphs of cluster algebras. https://arxiv.org/abs/2504.10245

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