## 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

$P$-partitions.

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