3 papers
math.CO2026
Geometric structures of -fans associated with rank cluster-cyclic exchange matrices
Ryota Akagi, Zhichao Chen
In this paper, we investigate the geometric structures of -fans associated with rank real cluster-cyclic exchange matrices. In this class, a simple recursion for tropical si…
math.RT2026
Real -, -structures and sign-coherence of cluster algebras
Ryota Akagi, Zhichao Chen
We generalize the theory of integer -, -matrices in cluster algebras to the real case. By a skew-symmetrizing method, we can reduce the problem of skew-symmetrizable patterns…
math.CO2025
Sign-coherence and tropical sign pattern for rank real cluster-cyclic exchange matrices
Ryota Akagi, Zhichao Chen
The sign-coherence about -vectors was conjectured by Fomin-Zelevinsky and solved completely by Gross-Hacking-Keel-Kontsevich for integer skew-symmetrizable case. We prove this c…