Bergman Complexes, Coxeter Arrangements, and Graph Associahedra
| dc.creator | Ardila, Federico | |
| dc.creator | Reiner, Victor | |
| dc.creator | Williams, Lauren | |
| dc.date | 2005-08-14 | |
| dc.date | 2005-09-14 | |
| dc.date.accessioned | 2026-07-07T05:22:21Z | |
| dc.date.available | 2026-07-07T05:22:21Z | |
| dc.description | 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. | |
| dc.description | 24 pages, 4 figures, new result and new proofs added | |
| dc.identifier | https://arxiv.org/abs/math/0508240 | |
| dc.identifier | http://arxiv.org/abs/math/0508240 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76031 | |
| dc.subject | Combinatorics | |
| dc.title | Bergman Complexes, Coxeter Arrangements, and Graph Associahedra | |
| dc.type | text |