Cyclic descents and P-partitions
| dc.creator | Petersen, T. Kyle | |
| dc.date | 2004-05-25 | |
| dc.date | 2005-05-10 | |
| dc.date.accessioned | 2026-07-07T05:08:34Z | |
| dc.date.available | 2026-07-07T05:08:34Z | |
| dc.description | Louis Solomon showed that the group algebra of the symmetric group $\mathfrak{S}_{n}$ 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. | |
| dc.description | 24 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/math/0405479 | |
| dc.identifier | http://arxiv.org/abs/math/0405479 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71314 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E99, 20F55, 06A07 | |
| dc.title | Cyclic descents and P-partitions | |
| dc.type | text |