The Bergman complex of a matroid and phylogenetic trees

Details The Bergman complex of a matroid and phylogenetic trees The Bergman complex of a matroid and phylogenetic trees

2003-11-21

arxiv.org/abs/math/0311370v2

Mathematics

Combinatorics

15 pages, 6 figures. Reorganized paper and updated references. To appear in J. Combin. Theory Ser. B

Scientific paper

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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