Shapes of RNA Pseudoknot Structures

In this article, we study abstract shapes of k-noncrossing, σ-canonical RNA pseudoknot structures. We consider lv1k- and lv5k-shapes, which represent a generalization of the abstract π'- and π-shapes of RNA secondary structures introduced by Giegerich et al. Using a novel approach, we compute the generating functions of lv1k- and lv5k-shapes as well as the generating functions of all lv1k- and lv5k-shapes induced by all k-noncrossing, σ-canonical RNA structures for fixed n. By means of singularity analysis of the generating functions, we derive explicit asymptotic expressions For online Supplementary Material, see www.liebertonline.com.