Asymptotic analysis of $k$-noncrossing matchings
| dc.creator | Jin, Emma Y. | |
| dc.creator | Reidys, Christian M. | |
| dc.creator | Wang, Rita R. | |
| dc.date | 2008-03-06 | |
| dc.date.accessioned | 2026-07-07T09:25:12Z | |
| dc.date.available | 2026-07-07T09:25:12Z | |
| dc.description | In this paper we study $k$-noncrossing matchings. A $k$-noncrossing matching is a labeled graph with vertex set $\{1,...,2n\}$ arranged in increasing order in a horizontal line and vertex-degree 1. The $n$ arcs are drawn in the upper halfplane subject to the condition that there exist no $k$ arcs that mutually intersect. We derive: (a) for arbitrary $k$, an asymptotic approximation of the exponential generating function of $k$-noncrossing matchings $F_k(z)$. (b) the asymptotic formula for the number of $k$-noncrossing matchings $f_{k}(n) \sim c_k n^{-((k-1)^2+(k-1)/2)} (2(k-1))^{2n}$ for some $c_k>0$. | |
| dc.description | 19 pages and 1 figure | |
| dc.identifier | https://arxiv.org/abs/0803.0848 | |
| dc.identifier | http://arxiv.org/abs/0803.0848 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156325 | |
| dc.subject | Combinatorics | |
| dc.subject | General Mathematics | |
| dc.subject | 05A16 | |
| dc.title | Asymptotic analysis of $k$-noncrossing matchings | |
| dc.type | text |