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arXiv · 0711.2346

$k$-noncrossing RNA structures with arc-length $\ge 3$

Emma Y. Jin·Christian M. Reidys
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Abstract

In this paper we enumerate $k$-noncrossing RNA pseudoknot structures with given minimum arc- and stack-length. That is, we study the numbers of RNA pseudoknot structures with arc-length $\ge 3$, stack-length $\ge σ$ and in which there are at most $k-1$ mutually crossing bonds, denoted by ${\sf T}_{k,σ}^{[3]}(n)$. In particular we prove that the numbers of 3, 4 and 5-noncrossing RNA structures with arc-length $\ge 3$ and stack-length $\ge 2$ satisfy ${\sf T}_{3,2}^{[3]}(n)^{}\sim K_3 n^{-5} 2.5723^n$, ${\sf T}^{[3]}_{4,2}(n)\sim K_4 n^{-{21/2}} 3.0306^n$, and ${\sf T}^{[3]}_{5,2}(n)\sim K_5 n^{-18} 3.4092^n$, respectively, where $K_3,K_4,K_5$ are constants. Our results are of importance for prediction algorithms for RNA pseudoknot structures.

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Emma Y. Jin, Christian M. Reidys. 2007-12-04. $k$-noncrossing RNA structures with arc-length $\ge 3$. https://arxiv.org/abs/0711.2346

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