  We show that the discretized configuration space of $k$ points in the
$n$-simplex is homotopy equivalent to a wedge of spheres of dimension $n-k+1$.
This space is homeomorphic to the order complex of the poset of ordered partial
partitions of $\{1,...,n+1\}$ with exactly $k$ parts. We compute the
exponential generating function for the Euler characteristic of this space in
two different ways, thereby obtaining a topological proof of a combinatorial
recurrence satisfied by the Stirling numbers of the second kind.
