Derived equivalence classification of m-cluster tilted algebras of type An

We use the maximal faces of the m-cluster complex of type An introduced in Fomin and Reading (2005) [9], to describe the m-cluster tilted algebras of type An as quivers with relations. We then classify connected components of m-cluster tilted algebras of type An up to derived equivalence using tilting complexes directly related to the combinatorics of the m-cluster complex of type An. This generalizes a result of Buan and Vatne (2008) [7].