Some coefficients of rank 2 cluster scattering diagrams

2025/07/29 by Akagi, Ryota
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.21916

Abstract

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 conjectures introduced by Thomas Elgin, Nathan Reading, and Salvatore Stella.

Citations

• Cluster scattering diagrams via quiver moduli and tight gradings
• Positivity of generalized cluster scattering diagrams
• Greedy elements in rank 2 cluster algebras
• Affine structures and non-archimedean analytic spaces

Related

• Cluster scattering coefficients in rank 2
• Cluster scattering diagrams via quiver moduli and tight gradings
• Explicit forms in lower degrees of rank 2 cluster scattering diagrams
• A combinatorial approach to scattering diagrams
• Consistency relations of rank 2 cluster scattering diagrams of affine type and pentagon relation