Combinatorics Of RNA Structures With Pseudoknots

2007/04/19 by Emma Y. Jin, Jing Qin, Jin, Emma Y. +3
Mathematics · #92E05 #Combinatorics (math.CO) #FOS: Mathematics #General Mathematics (math.GM) #math.CO #math.GM #msc:92E05

paper · pdf · doi:10.48550/arxiv.0704.2518

24 pages, 7 figures

arxiv created 2007/04/19 · arxiv updated 2009/12/01

Abstract

In this paper we derive the generating function of RNA structures with pseudoknots. We enumerate all k-noncrossing RNA pseudoknot structures categorized by their maximal sets of mutually intersecting arcs. In addition we enumerate pseudoknot structures over circular RNA. For 3-noncrossing RNA structures and RNA secondary structures we present a novel 4-term recursion formula and a 2-term recursion, respectively. Furthermore we enumerate for arbitrary k all k-noncrossing, restricted RNA structures i.e. k-noncrossing RNA structures without 2-arcs i.e. arcs of the form (i,i+2), for 1≤ i≤ n-2.

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• Asymptotic Enumeration of RNA Structures with Pseudoknots