On the decomposition of $k$-noncrossing RNA structures

Details On the decomposition of $k$-noncrossing RNA structures On the decomposition of $k$-noncrossing RNA structures

2009-02-22

arxiv.org/abs/0902.3783v1

Biology

Quantitative Biology

Biomolecules

15 figures, 22 pages

Scientific paper

An $k$-noncrossing RNA structure can be identified with an $k$-noncrossing diagram over $[n]$, which in turn corresponds to a vacillating tableaux having at most $(k-1)$ rows. In this paper we derive the limit distribution of irreducible substructures via studying their corresponding vacillating tableaux. Our main result proves, that the limit distribution of the numbers of irreducible substructures in $k$-noncrossing, $\sigma$-canonical RNA structures is determined by the density function of a $\Gamma(-\ln\tau_k,2)$-distribution for some $\tau_k<1$.

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