Pattern Avoidance and the Bruhat Order
| dc.creator | Tenner, Bridget Eileen | |
| dc.date | 2006-04-13 | |
| dc.date.accessioned | 2026-07-07T07:10:54Z | |
| dc.date.available | 2026-07-07T07:10:54Z | |
| dc.description | The structure of order ideals in the Bruhat order for the symmetric group is elucidated via permutation patterns. A method for determining non-isomorphic principal order ideals is described and applied for small lengths. The permutations with boolean principal order ideals are characterized. These form an order ideal which is a simplicial poset, and its rank generating function is computed. Moreover, the permutations whose principal order ideals have a form related to boolean posets are also completely described. It is determined when the set of permutations avoiding a particular set of patterns is an order ideal, and the rank generating functions of these ideals are computed. Finally, the Bruhat order in types B and D is studied, and the elements with boolean principal order ideals are characterized and enumerated by length. | |
| dc.description | 18 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/math/0604322 | |
| dc.identifier | http://arxiv.org/abs/math/0604322 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111568 | |
| dc.subject | Combinatorics | |
| dc.subject | 05E15; 06A07; 05A05 | |
| dc.title | Pattern Avoidance and the Bruhat Order | |
| dc.type | text |