The number of elements in the mutation class of a quiver of type $D_n$

Abstract

We show that the number of quivers in the mutation class of a quiver of Dynkin type $D_n$ is given by ${\sum }_{d|n}\varphi (n/d)\left(\genfrac{}{}{0ex}{}{2d}{d}\right)/(2n)$ for $n\ge 5$. To obtain this formula, we give a correspondence between the quivers in the mutation class and certain rooted trees.

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References in corpus (2)

• Counting cluster-tilted algebras of type $A_n$
• The mutation class of $D_n$ quivers