A branching rule for partition complexes

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

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