Changjian Fu, Shengfei Geng
Published 2024-07-16Version 1
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.
Comments: 28 pages, comments welcome
The enough $g$-pairs property and denominator vectors of cluster algebras
On denominator conjecture for cluster algebras of finite type
Quivers with potentials associated to triangulated surfaces, Part III: tagged triangulations and cluster monomials
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