5 M ay 2 00 4 CYCLIC AND AUGMENTED DESCENTS

Louis Solomon showed that the group algebra of the symmetric group Sn has a subalgebra called the descent algebra, generated by sums of permutations with a given descent set. In fact, he showed that every Coxeter group has something which can be called a descent algebra. For any Coxeter group that is also a Weyl group, Paola Cellini proved the existence of a different, commutative subalgebra of the group algebra. We derive the existence of such a commutative subalgebra for the cases of the symmetric group and of the hyperoctahedral group using a variation on Richard Stanley's theory of P-partitions.