Bergman Complexes, Coxeter Arrangements, and Graph Associahedra

Details Bergman Complexes, Coxeter Arrangements, and Graph Associahedra Bergman Complexes, Coxeter Arrangements, and Graph Associahedra

2005-08-14

arxiv.org/abs/math/0508240v2

Mathematics

Combinatorics

24 pages, 4 figures, new result and new proofs added

Scientific paper

Tropical varieties play an important role in algebraic geometry. The Bergman complex B(M) and the positive Bergman complex B+(M) of an oriented matroid M generalize to matroids the notions of the tropical variety and positive tropical variety associated to a linear ideal. Our main result is that if A is a Coxeter arrangement of type Phi with corresponding oriented matroid M_Phi, then B+(M_Phi) is dual to the graph associahedron of type Phi, and B(M_Phi) equals the nested set complex of A. In addition, we prove that for any orientable matroid M, one can find |mu(M)| different reorientations of M such that the corresponding positive Bergman complexes cover B(M), where mu(M) denotes the Mobius function of the lattice of flats of M.

Affiliated with

Also associated with

No associations

Rating

Bergman Complexes, Coxeter Arrangements, and Graph Associahedra 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 Bergman Complexes, Coxeter Arrangements, and Graph Associahedra, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bergman Complexes, Coxeter Arrangements, and Graph Associahedra will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-459698