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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…
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…
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…