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We study a circular order on labelled, m-edge-coloured trees with k vertices,and show that the set of such trees with a fixed circular order is in bijectionwith the set of RNA m-diagrams of degree k, combinatorial objects which can beregarded as RNA secondary structures of a certain kind. We enumerate these setsand show that the set of trees with a fixed circular order can be characterizedas an equivalence class for the transitive closure of an operation which, inthe case m=3, arises as an induction in the context of interval exchangetransformations.

A circular order on edge-coloured trees and RNA m-diagrams