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

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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 $\ge \sigma$ and in which there are at most $k-1$ mutually crossing bonds, denoted by ${\sf T} {k,\sigma}^{3}n$. 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.

Autor: Emma Y. Jin; Christian M. Reidys

Fuente: https://archive.org/