Counting the number of elements in the mutation classes of \(A_n\)-quivers (Q540100)

Summary: In this article we prove explicit formulae for the number of non-isomorphic cluster-tilted algebras of type \(\tilde A_n\) in the derived equivalence classes. In particular, we obtain the number of elements in the mutation classes of quivers of type \(\tilde A_n\). As a by-product, this provides an alternative proof for the number of quivers mutation equivalent to a quiver of Dynkin type \(D_n\) which was first determined by \textit{A.\,B. Buan} and \textit{H.\,A. Torkildsen} in [``The number of elements in the mutation class of a quiver of type \(D_n\), Electron. J. Comb. 16, No.\,1, Res. Paper R49, 23 p. (2009; Zbl 1175.16009)].