Shapes of RNA Pseudoknot Structures

In this article, we study abstract shapes of k-noncrossing, sigma-canonical RNA pseudoknot structures. We consider lv(k)(1)- and lv(k)(5)-shapes, which represent a generalization of the abstract pi- and pi-shapes of RNA secondary structures introduced by Giegerich et al. Using a novel approach, we compute the generating functions of lv(k)(1)- and lv(k)(5)-shapes as well as the generating functions of all lv(k)(1)- and lv(k)(5)-shapes induced by all k-noncrossing, sigma-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.