An explicit description of the colored mutation class of ${\tilde{\mathbb{A}}}_n$-quivers

Abstract

This paper addresses the combinatorial structure of $m$-colored mutation classes. We provide an explicit and purely combinatorial description of the $m$-colored quivers that arise within the $m$-colored mutation class of a quiver of type $\tilde{\mathbb{A}}$. Our results generalize and extend existing work, specifically recovering a description by Bastian [1] when the case $m=1$ is considered.