Sách Generating functions for permutations which contain a given descent set

Abstract
A large number of generating functions for permutation statistics can be ob-
tained by applying homomorphisms to simple symmetric function identities. In
particular, a large number of generating functions involving the number of descents
of a permutation σ, des(σ), arise in this way. For any given finite set S of positive
integers, we develop a method to produce similar generating functions for the set of
permutations of the symmetric group Sn whose descent set contains S. Our method
will be to apply certain homomorphisms to symmetric function identities involving
ribbon Schur functions.