Pseudoknot RNA structures with arc-length $\ge 4$
| dc.creator | Han, Hillary S. W. | |
| dc.creator | Reidys, Christian M. | |
| dc.date | 2008-03-10 | |
| dc.date | 2008-07-04 | |
| dc.date.accessioned | 2026-07-07T09:48:09Z | |
| dc.date.available | 2026-07-07T09:48:09Z | |
| dc.description | 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 $\sum_{n\ge 0}{\sf T}_{k}^{[4]}(n)z^n$ 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 $4\le k\le 9$. | |
| dc.description | 18 pages; 3 figures | |
| dc.identifier | https://arxiv.org/abs/0803.1399 | |
| dc.identifier | http://arxiv.org/abs/0803.1399 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/164106 | |
| dc.subject | Combinatorics | |
| dc.subject | 00A71 | |
| dc.title | Pseudoknot RNA structures with arc-length $\ge 4$ | |
| dc.type | text |