  We study filters in the partition lattice formed by restricting to partitions
by type. The M\"obius function is determined in terms of the easier-to-compute
descent set statistics on permutations and the M\"obius function of filters in
the lattice of integer compositions. When the underlying integer partition is a
knapsack partition, the M\"obius function on integer compositions is determined
by a topological argument. In this proof the permutahedron makes a cameo
appearance.
