7 papers
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…
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…
Fractal phenomenon in - and -vectors of the Markov quiver
Ryota Akagi, Zhichao Chen
We study the - and -patterns associated with rank skew-symmetrizable matrices of -invariant type, including the Markov quiver. Motivated by the self-contained simple m…
Relation between generalized and ordinary cluster algebras
Ryota Akagi, Tomoki Nakanishi
Recently, Ramos and Whiting showed that any generalized cluster algebra of geometric type is isomorphic to a quotient of a subalgebra of a certain cluster algebra. Based on their i…
Some coefficients of rank 2 cluster scattering diagrams
Ryota Akagi
The purpose of this paper is to translate the expression of rank 2 cluster scattering diagrams via dilogarithm elements into via formal power series. As a corollary, we prove some…
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…