Bruhat intervals as rooks on skew Ferrers boards
| dc.creator | Sjostrand, Jonas | |
| dc.date | 2006-01-25 | |
| dc.date.accessioned | 2026-07-07T06:59:17Z | |
| dc.date.available | 2026-07-07T06:59:17Z | |
| dc.description | We characterise the permutations pi such that the elements in the closed lower Bruhat interval [id,pi] of the symmetric group correspond to non-taking rook configurations on a skew Ferrers board. It turns out that these are exactly the permutations pi such that [id,pi] corresponds to a flag manifold defined by inclusions, studied by Gasharov and Reiner. Our characterisation connects the Poincare polynomials (rank-generating function) of Bruhat intervals with q-rook polynomials, and we are able to compute the Poincare polynomial of some particularly interesting intervals in the finite Weyl groups A_n and B_n. The expressions involve q-Stirling numbers of the second kind. As a by-product of our method, we present a new Stirling number identity connected to both Bruhat intervals and the poly-Bernoulli numbers defined by Kaneko. | |
| dc.description | 16 pages, 9 figures | |
| dc.identifier | https://arxiv.org/abs/math/0601615 | |
| dc.identifier | http://arxiv.org/abs/math/0601615 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107695 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 05A15; 06A07, 14M15 | |
| dc.title | Bruhat intervals as rooks on skew Ferrers boards | |
| dc.type | text |