Flag arrangements and triangulations of products of simplices

Details Flag arrangements and triangulations of products of simplices Flag arrangements and triangulations of products of simplices

2006-05-22

arxiv.org/abs/math/0605598v1

Mathematics

Combinatorics

39 pages, 12 figures, best viewed in color

Scientific paper

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 \Delta_{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.

Affiliated with

Also associated with

No associations

Rating

Flag arrangements and triangulations of products of simplices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Flag arrangements and triangulations of products of simplices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Flag arrangements and triangulations of products of simplices will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-181955