From Bruhat intervals to intersection lattices and a conjecture of Postnikov
| dc.creator | Hultman, Axel | |
| dc.creator | Linusson, Svante | |
| dc.creator | Shareshian, John | |
| dc.creator | Sjöstrand, Jonas | |
| dc.date | 2007-10-05 | |
| dc.date.accessioned | 2026-07-07T08:34:24Z | |
| dc.date.available | 2026-07-07T08:34:24Z | |
| dc.description | We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation $w\in \Sn$ is at most the number of elements below $w$ in the Bruhat order, and (B) that equality holds if and only if $w$ avoids the patterns 4231, 35142, 42513 and 351624. Furthermore, assertion (A) is extended to all finite reflection groups. A byproduct of this result and its proof is a set of inequalities relating Betti numbers of complexified inversion arrangements to Betti numbers of closed Schubert cells. Another consequence is a simple combinatorial interpretation of the chromatic polynomial of the inversion graph of a permutation which avoids the above patterns. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0710.1220 | |
| dc.identifier | http://arxiv.org/abs/0710.1220 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/139426 | |
| dc.subject | Combinatorics | |
| dc.title | From Bruhat intervals to intersection lattices and a conjecture of Postnikov | |
| dc.type | text |