Permutation resolutions for Specht modules

For every composition λ of a positive integer r , we construct a finite chain complex whose terms are direct sums of permutation modules M for the symmetric group Sr with Young subgroup stabilizers Sμ. The construction is combinatorial and can be carried out over every commutative base ring k. We conjecture that for every partition λ the chain complex has homology concentrated in one degree (at the end of the complex) and that it is isomorphic to the dual of the Specht module S. We prove the exactness in special cases.