4 papers
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 solved completely by Gross-Hacking-Keel-Kontsevich for integer skew-symmetrizable case. We prove this c…
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…