Some coefficients of rank 2 cluster scattering diagrams

TL;DR

This paper translates rank 2 cluster scattering diagrams into formal power series and proves related conjectures, advancing understanding of their algebraic structure.

Contribution

It introduces a new formal power series approach to rank 2 cluster scattering diagrams and confirms conjectures by Elgin, Reading, and Stella.

Findings

Successful translation of diagrams into formal power series

Proof of conjectures related to rank 2 cluster scattering diagrams

Enhanced algebraic understanding of cluster scattering structures

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.