Descent algebras, hyperplane arrangements, and shuffling cards
| dc.creator | Fulman, Jason | |
| dc.date | 1998-01-20 | |
| dc.date | 1999-07-15 | |
| dc.date.accessioned | 2026-07-07T05:23:37Z | |
| dc.date.available | 2026-07-07T05:23:37Z | |
| dc.description | Two notions of riffle shuffling on finite Coxeter groups are given: one using Solomon's descent algebra and another using random walk on chambers of hyperplane arrangements. These coincide for types $A$,$B$,$C$, $H_3$, and rank two groups. Both notions have the same, simple eigenvalues. The hyperplane definition is especially natural and satisfies a positivity property when $W$ is crystallographic and the relevant parameter is a good prime. The hyperplane viewpoint suggests interesting connections with Lie theory and leads to a notion of riffle shuffling for arbitrary real hyperplane arrangements and oriented matroids. Connections with Cellini's descent algebra are given. | |
| dc.identifier | https://arxiv.org/abs/math/9801089 | |
| dc.identifier | http://arxiv.org/abs/math/9801089 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76513 | |
| dc.subject | Combinatorics | |
| dc.subject | Group Theory | |
| dc.subject | 20G40;20F55 | |
| dc.title | Descent algebras, hyperplane arrangements, and shuffling cards | |
| dc.type | text |