The Bergman complex of a matroid and phylogenetic trees
Combinatorics
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0311370,
title = {The Bergman complex of a matroid and phylogenetic trees},
author = {Federico Ardila and Carly Klivans},
journal= {arXiv preprint arXiv:math/0311370},
year = {2007}
}
Comments
15 pages, 6 figures. Reorganized paper and updated references. To appear in J. Combin. Theory Ser. B