Irreducibility in RNA structures

In this paper we study irreducibility in RNA structures. By RNA structure we mean RNA secondary as well as RNA pseudoknot structures. In our analysis we shall contrast random and minimum free energy (mfe) configurations. We compute various distributions: of the numbers of irreducible substructures, their locations and sizes, parameterized in terms of the maximal number of mutually crossing arcs, $k-1$, and the minimal size of stacks $\sigma$. In particular, we analyze the size of the largest irreducible substructure for random and mfe structures, which is the key factor for the folding time of mfe configurations.