Counting the number of elements in the mutation classes of Ãn-quivers

Abstract

In this article we prove explicit formulae for the number of non-isomorphic cluster-tilted algebras of type Ãn in the derived equivalence classes. In particular, we obtain the number of elements in the mutation classes of quivers of type Ãn. As a by-product, this provides an alternative proof for the number of quivers mutation equivalent to a quiver of Dynkin type Dn which was first determined by Buan and Torkildsen in [5].