2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164106In 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 $\sum_{n\ge 0}{\sf T}_{k}^{[4]}(n)z^n$ and (b) derive for $k\le 9$ the asymptotic formula ${\sf T}_{k}^{[4]}(n)\sim c_k n^{-((k-1)^2+(k-1)/2)} γ_k^{-n}$. Furthermore we explicitly compute the exponential growth rates $γ_k^{-1}$ and asymptotic formulas for $4\le k\le 9$.18 pages; 3 figuresCombinatorics00A71text