The coloured mutation class of \(\mathbb {A}_n\)-quivers

In this paper we give an explicit and purely combinatorial description of the m-coloured quivers that appears in the m-coloured mutation class of a quiver of type \(\mathbb {A}_n\) ${\mathbb{A}}_n$ . The m-coloured mutation defined by Buan and Thomas in (Adv Math 222(3):971–995, 2009) generalizes the well-known quiver mutation of Fomin and Zelevinsky (J Am Math Soc 15(2):497–529, 2002). In particular, our description generalizes a result of Buan and Vatne (J Algebra 319(7):2723–2738, 2008), which we recover when \(m=1\) $m=1$ .