Pseudoknot RNA structures with arc-length $\ge 4$

Abstract

In this paper we study $k$-noncrossing RNA structures with minimum arc-length 4 and at most $k-1$ mutually crossing bonds. Let ${\mathsf{T}}_k^{[4]}(n)$ denote the number of $k$-noncrossing RNA structures with arc-length $\ge 4$ over $n$ vertices. We prove (a) a functional equation for the generating function ${\sum }_{n\ge 0}{\mathsf{T}}_k^{[4]}(n)z^n$ and (b) derive for $k\le 9$ the asymptotic formula ${\mathsf{T}}_k^{[4]}(n)\sim c_k{n}^{-((k-1{)}^2+(k-1)/2)}{\gamma }_k^{-n}$. Furthermore we explicitly compute the exponential growth rates ${\gamma }_k^{-1}$ and asymptotic formulas for $4\le k\le 9$.

18 pages; 3 figures

References in corpus (1)

• RNA-LEGO: Combinatorial Design of Pseudoknot RNA