Pseudoknot RNA structures with arc-length ≥ 4

2008/03/10 by Hillary S. W. Han, Han, Hillary S. W., Christian M. Reidys +1
Mathematics · #00A71 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:00A71

paper · pdf · doi:10.48550/arxiv.0803.1399

18 pages; 3 figures

arxiv created 2008/07/04 · arxiv updated 2009/12/01

Abstract

In this paper we study k-noncrossing RNA structures with minimum arc-length 4 and at most k-1 mutually crossing bonds. Let \sf T_k^[4](n) denote the number of k-noncrossing RNA structures with arc-length ≥ 4 over n vertices. We prove (a) a functional equation for the generating function ∑_{n≥ 0}\sf T_k^[4](n)zⁿ and (b) derive for k≤ 9 the asymptotic formula \sf T_k^[4](n)∼ c_k n^{-((k-1)2+(k-1)/2)} γ_k^-n. Furthermore we explicitly compute the exponential growth rates γ_k^-1 and asymptotic formulas for 4≤ k≤ 9.

Related

• k-noncrossing RNA structures with arc-length ≥ 3
• Canonical RNA pseudoknot structures
• Pseudoknot RNA Structures with Arc-Length ≥ 3
• Asymptotic Enumeration of RNA Structures with Pseudoknots
• Central and Local Limit Theorems for RNA Structures