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- W2949125440 abstract "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. The positive Bergman complex is defined so that given a linear ideal I with associated oriented matroid M_I, the positive tropical variety associated to I is equal to the fan over B+(M_I). Our main result is that a certain 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 K_n, we show that the face poset of the subdivision of B+(K_n) is dual to the face poset of the associahedron A_{n-2}, and we give a formula for the number of fine cells within a coarse cell." @default.
- W2949125440 created "2019-06-27" @default.
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- W2949125440 date "2004-06-07" @default.
- W2949125440 modified "2023-09-26" @default.
- W2949125440 title "The Positive Bergman Complex of an Oriented Matroid" @default.
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