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The Bergman complex of a matroid and phylogenetic trees

Federico Ardila·Carly Klivans
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Abstract

We study the Bergman complex B(M) of a matroid M: a polyhedral complex which arises in algebraic geometry, but which we describe purely combinatorially. We prove that a natural subdivision of the Bergman complex of M is a geometric realization of the order complex of its lattice of flats. In addition, we show that the Bergman fan B'(K_n) of the graphical matroid of the complete graph K_n is homeomorphic to the space of phylogenetic trees T_n.

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Federico Ardila, Carly Klivans. 2005-05-04. The Bergman complex of a matroid and phylogenetic trees. https://arxiv.org/abs/math/0311370

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