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تسجيل مستخدم جديدStacks in canonical RNA pseudoknot structures
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In this paper we study the distribution of stacks in $k$-noncrossing, $tau$-canonical RNA pseudoknot structures ($<k,tau> $-structures). An RNA structure is called $k$-noncrossing if it has no more than $k-1$ mutually crossing arcs and $tau$-canonical if each arc is contained in a stack of length at least $tau$. Based on the ordinary generating function of $<k,tau>$-structures cite{Reidys:08ma} we derive the bivariate generating function ${bf T}_{k,tau}(x,u)=sum_{n geq 0} sum_{0leq t leq frac{n}{2}} {sf T}_{k, tau}^{} (n,t) u^t x^n$, where ${sf T}_{k,tau}(n,t)$ is the number of $<k,tau>$-structures having exactly $t$ stacks and study its singularities. We show that for a certain parametrization of the variable $u$, ${bf T}_{k,tau}(x,u)$ 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.
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