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EJC
2006

The positive Bergman complex of an oriented matroid

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The positive Bergman complex of an oriented matroid
We study the positive Bergman complex B+ (M) of an oriented matroid M, which is a certain subcomplex of the Bergman complex B(M) of the underlying unoriented matroid M. The positive Bergman complex is defined so that given a linear ideal I with associated oriented matroid MI , the positive tropical variety associated to I is equal to the fan over B+ (MI ). Our main result is that a certain "fine" subdivision of B+ (M) is a geometric realization of the order complex of the proper part of the Las Vergnas face lattice of M. It follows that B+ (M) is homeomorphic to a sphere. For the oriented matroid of the complete graph Kn, we show that the face poset of the "coarse" subdivision of B+ (Kn) is dual to the face poset of the associahedron An-2, and we give a formula for the number of fine cells within a coarse cell.
Federico Ardila, Caroline J. Klivans, Lauren Willi
Added 12 Dec 2010
Updated 12 Dec 2010
Type Journal
Year 2006
Where EJC
Authors Federico Ardila, Caroline J. Klivans, Lauren Williams
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