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<p>The statement in the title was proved in [<CitationRef CitationID="CR1">1</CitationRef>] 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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年9月4日

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  • Shuhao Deng,
  • Changjian Fu

摘要

The statement in the title was proved in [1] 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.