Efficient Counting and Asymptotics of $k$-noncrossing tangled-diagrams
| dc.creator | Chen, William Y. C. | |
| dc.creator | Qin, Jing | |
| dc.creator | Reidys, Christian M. | |
| dc.creator | Zeilberger, Doron | |
| dc.date | 2008-02-24 | |
| dc.date.accessioned | 2026-07-07T09:22:57Z | |
| dc.date.available | 2026-07-07T09:22:57Z | |
| dc.description | In this paper we enumerate $k$-noncrossing tangled-diagrams. A tangled-diagram is a labeled graph whose vertices are $1,...,n$ have degree $\le 2$, and are arranged in increasing order in a horizontal line. Its arcs are drawn in the upper halfplane with a particular notion of crossings and nestings. Our main result is the asymptotic formula for the number of $k$-noncrossing tangled-diagrams $T_{k}(n) \sim c_k n^{-((k-1)^2+(k-1)/2)} (4(k-1)^2+2(k-1)+1)^n$ for some $c_k>0$. | |
| dc.description | 9 pages and 2 figures | |
| dc.identifier | https://arxiv.org/abs/0802.3491 | |
| dc.identifier | http://arxiv.org/abs/0802.3491 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155561 | |
| dc.subject | Combinatorics | |
| dc.subject | 05A16 | |
| dc.title | Efficient Counting and Asymptotics of $k$-noncrossing tangled-diagrams | |
| dc.type | text |