AbstractA large number of generating functions for permutation statistics can be ob-tained by applying homomorphisms to simple symmetric function identities. Inparticular, a large number of generating functions involving the number of descentsof a permutation σ, des(σ), arise in this way. For any given finite set S of positiveintegers, we develop a method to produce similar generating functions for the set ofpermutations of the symmetric group Sn whose descent set contains S. Our methodwill be to apply certain homomorphisms to symmetric function identities involvingribbon Schur functions...