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Denominator conjecture for some surface cluster algebras
Changjian Fu, Shengfei Geng · 2024-07-16 · via math.CO updates on arXiv.org

The denominator conjecture, proposed by Fomin and Zelevinsky, says that for a cluster algebra, the cluster monomials are uniquely determined by their denominator vectors with respect to an initial cluster. In this paper, for a cluster algebra from a marked surface with at least three boundary marked points, we establish this conjecture with respect to a given strong admissible tagged triangulation.

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