Bergman Complexes, Coxeter Arrangements, and Graph Associahedra

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

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Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/76031

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0508240
 http://arxiv.org/abs/math/0508240

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arXiv