Geodesic
The colored Eulerian descent algebra
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 3, pp. 671-694.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Using a new colored analogue of $P$-partitions, we prove the existence of a colored Eulerian descent algebra which is a subalgebra of the Mantaci-Reutenauer algebra. This algebra has a basis consisting of formal sums of colored permutations with the same number of descents (using Steingrímsson's definition of the descent set of a colored permutation). The colored Eulerian descent algebra extends familiar Eulerian descent algebras from the symmetric group algebra and the hyperoctahedral group algebra to colored permutation group algebras. We also describe orthogonal idempotents that span the colored Eulerian descent algebra and include, as a special case, the familiar Eulerian idempotents in the group algebra of the symmetric group.
Classification : 05E15, 06A07, 06A11
Keywords: colored posets, colored $P$-partitions, colored Eulerian descent algebra, Mantaci-Reutenauer algebra 
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     author = {Moynihan, Matthew},
     title = {The colored {Eulerian} descent algebra},
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Moynihan, Matthew. The colored Eulerian descent algebra. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 3, pp. 671-694. http://geodesic.mathdoc.fr/item/JAC_2015__42_3_a11/