1 citations · 1 across the 8 of their papers we have counts for
8 papers
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…
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…
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…
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 proved by Gross-Hacking-Keel-Kontsevich for integer skew-symmetrizable case. We prove this conjecture a…
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…
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…
Cluster-cyclic condition of skew-symmetrizable matrices of rank 3 via the Markov constant
Ryota Akagi
In this paper, we consider mutations of skew-symmetrizable matrices of rank 3. Every skew-symmetrizable matrix corresponds to a weighted quiver, and we study the conditions when th…
Explicit forms in lower degrees of rank 2 cluster scattering diagrams
Ryota Akagi
In this paper, we study wall elements of rank 2 cluster scattering diagrams based on dilogarithm elements. We derive two major results. First, we give a method to calculate wall el…