2008/07/04 by Hillary S. W. Han, Han, Hillary S. W., Christian M. Reidys +1
Biochemistry, Genetics and Molecular Biology · Mathematics · #05A15 #Combinatorics (math.CO) #FOS: Mathematics #General Mathematics (math.GM) #Genomics and Chromatin Dynamics #RNA Research and Splicing #RNA and protein synthesis mechanisms #math.CO #math.GM #msc:05A15
paper · pdf · doi:10.48550/arxiv.0807.0689
19pages, 4 figures
arxiv created 2008/07/04 · openalex publication_date 2008/07/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the distribution of stacks in k-noncrossing, τ-canonical RNA pseudoknot structures (<k,τ> -structures). An RNA structure is called k-noncrossing if it has no more than k-1 mutually crossing arcs and τ-canonical if each arc is contained in a stack of length at least τ. Based on the ordinary generating function of <k,τ>-structures \citeReidys:08ma we derive the bivariate generating function \bf Tk,τ(x,u)=∑n ≥ 0 ∑0≤ t ≤ (n)/(2) \sf Tk, τ (n,t) ut xn, where \sf Tk,τ(n,t) is the number of <k,τ>-structures having exactly t stacks and study its singularities. We show that for a certain parametrization of the variable u, \bf Tk,τ(x,u) has a unique, dominant singularity. The particular shift of this singularity parametrized by u implies a central limit theorem for the distribution of stack-numbers. Our results are of importance for understanding the ``language'' of minimum-free energy RNA pseudoknot structures, generated by computer folding algorithms.