Enumeration of totally positive Grassmann cells
| dc.creator | Williams, Lauren K. | |
| dc.date | 2003-07-20 | |
| dc.date | 2004-03-13 | |
| dc.date.accessioned | 2026-07-07T04:59:47Z | |
| dc.date.available | 2026-07-07T04:59:47Z | |
| dc.description | Alex Postnikov has given a combinatorially explicit cell decomposition of the totally nonnegative part of a Grassmannian, denoted Gr_{kn}+, and showed that this set of cells is isomorphic as a graded poset to many other interesting graded posets. The main result of this paper is an explicit generating function which enumerates the cells in Gr_{kn}+ according to their dimension. As a corollary, we give a new proof that the Euler characteristic of Gr_{kn}+ is 1. Additionally, we use our result to produce a new q-analog of the Eulerian numbers, which interpolates between the Eulerian numbers, the Narayana numbers, and the binomial coefficients. | |
| dc.description | 21 pages, 10 figures. Final version, with references added and minor corrections made, to appear in Advances in Mathematics | |
| dc.identifier | https://arxiv.org/abs/math/0307271 | |
| dc.identifier | http://arxiv.org/abs/math/0307271 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68127 | |
| dc.subject | Combinatorics | |
| dc.subject | 05Exx; 05Axx | |
| dc.title | Enumeration of totally positive Grassmann cells | |
| dc.type | text |