Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Bergman complex of a matroid and phylogenetic trees   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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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
30
The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: plasm-ph