Cyclic descents and P-partitions

2004/05/25 by T. Kyle Petersen, Petersen, T. Kyle
Computer Science · Mathematics · #05E99 #06A07 #20F55 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E99 #msc:06A07 #msc:20F55

paper · pdf · doi:10.48550/arxiv.math/0405479

24 pages, 8 figures

openalex publication_date 2004/05/25 · arxiv created 2005/05/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Louis Solomon showed that the group algebra of the symmetric group \mathfrakS_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.

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