Journal of Algebraic Combinatorics

, Volume 22, Issue 3, pp 343–375 | Cite as

Cyclic Descents and P-Partitions

  • T. Kyle PetersenEmail author


Louis Solomon showed that the group algebra of the symmetric group \(\mathfrak{S}_{n}\) 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.


descent algebra P-partition 


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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of MathematicsBrandeis UniversityWalthamUSA

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