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) .
We develop and study the structure of combinatorial objects that are a special case of RNA secondary structures. These are generalisations of objects arising from interval exchange transformations generalising those in the Sturmian context. We represent them as labelled edge-coloured trees. 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 .
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that are a special case of RNA secondary structures. These are generalisations of objects
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. We
generalising those in the Sturmian context. We represent them as labelled edge-coloured trees. We
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these objects and further
them and
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of these objects is in natural
is in
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(in the cluster algebra sense)
. Furthermore, we interpret a notion of induction used to model generalised interval exchange transformations as a composition of cluster mutations