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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 $ge 4$ over $n$ vertices. We prove (a) a functional equation for the generating function $sum_{nge 0}{sf T}_{k}^{[4]}(n)z^n$ and (b) derive for $kle 9$ the asymptotic formula ${sf T}_{k}^{[4]}(n)sim c_k n^{-((k-1)^2+(k-1)/2)} gamma_k^{-n}$. Furthermore we explicitly compute the exponential growth rates $gamma_k^{-1}$ and asymptotic formulas for $4le kle 9$.
In this paper we enumerate $k$-noncrossing RNA pseudoknot structures with given minimum arc- and stack-length. That is, we study the numbers of RNA pseudoknot structures with arc-length $ge 3$, stack-length $ge sigma$ and in which there are at most $
In this paper we study $k$-noncrossing, canonical RNA pseudoknot structures with minimum arc-length $ge 4$. Let ${sf T}_{k,sigma}^{[4]} (n)$ denote the number of these structures. We derive exact enumeration results by computing the generating functi
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 $tau$-canonica
In this paper we present a selfcontained analysis and description of the novel {it ab initio} folding algorithm {sf cross}, which generates the minimum free energy (mfe), 3-noncrossing, $sigma$-canonical RNA structure. Here an RNA structure is 3-nonc
In this paper we analyze the length-spectrum of blocks in $gamma$-structures. $gamma$-structures are a class of RNA pseudoknot structures that plays a key role in the context of polynomial time RNA folding. A $gamma$-structure is constructed by nesti