On the decomposition of k-noncrossing RNA structures

A k-noncrossing RNA structure can be identified with a k-noncrossing diagram over [n], which in turn corresponds to a vacillating tableau having at most (k−1) rows. In this paper we derive the limit distribution of irreducible substructures via studying their corresponding vacillating tableaux. Our main result proves, that the limit distribution of the numbers of irreducible substructures in k-noncrossing, σ-canonical RNA structures is determined by the density function of a -distribution for some τ_k>1.