On the decomposition of $k$-noncrossing RNA structures

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 $\tau_k<1$.

💡 Research Summary

The paper investigates the combinatorial and probabilistic properties of k‑noncrossing RNA secondary structures, focusing on the distribution of their irreducible substructures. A k‑noncrossing diagram is a set of arcs drawn over the ordered set