Descent algebras and P-partitions

   Kyle Petersen,  (Brandeis U., Boston)

Louis Solomon showed that the group algebra of the
symmetric group has a subalgebra called the descent
algebra, generated by sums of permutations with a
given descent set. For any 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
case of the symmetric group and of the hyperoctahedral
group using a variation on Richard Stanley's theory of

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