Pseudoknot RNA Structures with Arc-Length ≥4

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Abstract
In this article, we study k-noncrossing RNA structures with minimum arc-length 4 and at most k − 1 mutually crossing bonds. Let Tk[4](n) denote the number of k-noncrossing RNA structures with arc-length ≥4 over n vertices. We (a) prove a functional equation for the generating function ∑n≥0 Tk[4](n)zn and (b) derive for 4 ≤ k ≤ 9 the asymptotic formula Tk[4](n) ∼ ck n−((k−1)2+(k−1)/2) γk−n. Furthermore, we explicitly compute the exponential growth rates γk−1 and asymptotic formulas for 4 ≤ k ≤ 9.

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