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math.RT2024
On denominator conjecture for cluster algebras of finite type
Changjian Fu, Shengfei Geng
We continue our investigation on denominator conjecture of Fomin and Zelevinsky for cluster algebras via geometric models initialed in \cite{FG22}. In this paper, we confirm the de…
math.RT2024
Denominator conjecture for some surface cluster algebras
Changjian Fu, Shengfei Geng
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 respe…
math.RT2024
On -tilting graphs for quasi-silted algebras
Wei Dai, Changjian Fu, Shengfei Geng +1
We prove that the -tilting graph of any quasi-silted algebra is connected and has the reachable-in-face property. Our approach utilizes -reduction and wall and chamber struct…