A combinatorial framework for RNA tertiary interaction
| dc.creator | Qin, Jing | |
| dc.creator | Reidys, Christian M. | |
| dc.date | 2007-10-18 | |
| dc.date | 2007-12-08 | |
| dc.date.accessioned | 2026-07-07T08:47:51Z | |
| dc.date.available | 2026-07-07T08:47:51Z | |
| dc.description | In this paper we show how to express RNA tertiary interactions via the concepts of tangled diagrams. Tangled diagrams allow to formulate RNA base triples and pseudoknot-interactions and to control the maximum number of mutually crossing arcs. In particular we study two subsets of tangled diagrams: 3-noncrossing tangled-diagrams with $\ell$ vertices of degree two and 2-regular, 3-noncrossing partitions (i.e. without arcs of the form $(i,i+1)$). Our main result is an asymptotic formula for the number of 2-regular, 3-noncrossing partitions, denoted by $p_{3,2}(n)$, 3-noncrossing partitions over $[n]$. The asymptotic formula is derived by the analytic theory of singular difference equations due to Birkhoff-Trjitzinsky. Explicitly, we prove the formula $p_{3,2}(n+1)\sim K 8^{n}n^{-7}(1+c_{1}/n+c_{2}/n^2+c_3/n^3)$ where $K,c_i$, $i=1,2,3$ are constants. | |
| dc.description | 21 pages, 19 figures | |
| dc.identifier | https://arxiv.org/abs/0710.3523 | |
| dc.identifier | http://arxiv.org/abs/0710.3523 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143746 | |
| dc.subject | Combinatorics | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 47N60 | |
| dc.title | A combinatorial framework for RNA tertiary interaction | |
| dc.type | text |