Before revision: We develop and study the structure of combinatorial objects  arising from interval exchange transformations . 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 develop and study the structure of combinatorial objects arising from interval exchange transformations generalising those in the Sturmian context. We represent them as labelled edge-coloured trees. 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) .