The Möbius function of partitions with restricted block sizes

The purpose of this paper is to compute the Möbius function of filters in the partition lattice formed by restricting to partitions by type. The Möbius function is determined in terms of the descent set statistics on permutations and the Möbius function of filters in the lattice of integer compositions. When the underlying integer partition is a knapsack partition, the Möbius function on integer compositions is determined by a topological argument. In this proof the permutahedron makes a cameo appearance.