  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 $c_k>0$.
