Mathematics – Combinatorics
Scientific paper
2004-11-11
Mathematics
Combinatorics
22 pages, 3 figures
Scientific paper
The tropical variety defined by linear equations with constant coefficients is the Bergman fan of the corresponding matroid. Building on a self-contained introduction to matroid polytopes, we present a geometric construction of the Bergman fan, and we discuss its relationship with the simplicial complex of nested sets in the lattice of flats. The Bergman complex is triangulated by the nested set complex, and the two complexes coincide if and only if every connected flat remains connected after contracting along any subflat. This sharpens a result of Ardila-Klivans who showed that the Bergman complex is triangulated by the order complex of the lattice of flats. The nested sets specify the De Concini-Procesi compactification of the complement of a hyperplane arrangement, while the Bergman fan specifies the tropical compactification. These two compactifications are almost equal, and we highlight the subtle differences.
Feichtner Eva Maria
Sturmfels Bernd
No associations
LandOfFree
Matroid polytopes, nested sets and Bergman fans 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 Matroid polytopes, nested sets and Bergman fans, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Matroid polytopes, nested sets and Bergman fans will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-274051