The Bergman complex of a matroid and phylogenetic trees
نویسندگان
چکیده
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 B̃(Kn) of the graphical matroid of the complete graph Kn is homeomorphic to the space of phylogenetic trees Tn.
منابع مشابه
Subdominant matroid ultrametrics
Given a matroid M on the ground set E, the Bergman fan B̃(M), or space of M -ultrametrics, is a polyhedral complex in RE which arises in several different areas, such as tropical algebraic geometry, dynamical systems, and phylogenetics. Motivated by the phylogenetic situation, we study the following problem: Given a point ω in RE , we wish to find an M -ultrametric which is closest to it in the ...
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 96 شماره
صفحات -
تاریخ انتشار 2006