Before revision:  We classify and enumerate these objects and further show that a natural subset of these objects is in natural bijection with a set of m-clusters (in the cluster algebra sense) .
After revision:  We classify and enumerate these objects and further show that a natural subset of these objects is in natural 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 .