Before revision:  We classify and enumerate them and show that a natural subset is in bijection with a set of m-clusters. Furthermore, we interpret a notion of induction used to model generalised interval exchange transformations as a composition of cluster mutations .
After revision:  We classify and enumerate them and show that the set of trees with a fixed circular order can be characterized as an equivalence class for the transitive closure of an operation which, in the case m=3, arises as an induction in the context of interval exchange transformations as a composition of cluster mutations .