  Let $S_n$ be the symmetric group, and let $Y$ be a Young subgroup of $S_n$.
Let $\Pi_n$ be the complex of partitions of $\{1, \ldots, n\}$. Our main result
is a $Y$-equivariant decomposition of $\Pi_n$. As an application, we obtain new
information about the quotient space of $|\Pi_n|$ by a Young subgroup.
