Flag arrangements and triangulations of products of simplices
| dc.creator | Ardila, Federico | |
| dc.creator | Billey, Sara | |
| dc.date | 2006-05-22 | |
| dc.date.accessioned | 2026-07-07T07:14:27Z | |
| dc.date.available | 2026-07-07T07:14:27Z | |
| dc.description | We investigate the line arrangement that results from intersecting d complete flags in C^n. We give a combinatorial description of the matroid T_{n,d} that keeps track of the linear dependence relations among these lines. We prove that the bases of the matroid T_{n,3} characterize the triangles with holes which can be tiled with unit rhombi. More generally, we provide evidence for a conjectural connection between the matroid T_{n,d}, the triangulations of the product of simplices Delta_{n-1} x Δ_{d-1}, and the arrangements of d tropical hyperplanes in tropical (n-1)-space. Our work provides a simple and effective criterion to ensure the vanishing of many Schubert structure constants in the flag manifold, and a new perspective on Billey and Vakil's method for computing the non-vanishing ones. | |
| dc.description | 39 pages, 12 figures, best viewed in color | |
| dc.identifier | https://arxiv.org/abs/math/0605598 | |
| dc.identifier | http://arxiv.org/abs/math/0605598 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/112883 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 52C35; 05B35; 14M15; 52C22; 52C20 | |
| dc.title | Flag arrangements and triangulations of products of simplices | |
| dc.type | text |