Cyclic descents and $P$-partitions.
Journal of Algebraic Combinatorics, Tome 22 (2005) no. 3, pp. 343-375.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: Louis Solomon showed that the group algebra of the symmetric group $\mathfrak S _{ n}$ mathfrakS_n $_{ n}$ 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 that can be called a descent algebra. There is also a commutative, semisimple subalgebra of Solomon's descent algebra generated by sums of permutations with the same number of descents: an "Eulerian" descent algebra. For any Coxeter group that is also a Weyl group, Paola Cellini proved the existence of a different Eulerian subalgebra based on a modified definition of descent. We derive the existence of Cellini's subalgebra for the case of the symmetric group and of the hyperoctahedral group using a variation on Richard Stanley's theory of $P$-partitions.
Mots-clés : keywords descent algebra, $P$-partition 
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Petersen, T.Kyle. Cyclic descents and $P$-partitions.. Journal of Algebraic Combinatorics, Tome 22 (2005) no. 3, pp. 343-375. https://geodesic-test.mathdoc.fr/item/JAC_2005__22_3_a0/