37,770 research outputs found
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.Comment: 15 pages, 6 figures. Reorganized paper and updated references. To
appear in J. Combin. Theory Ser.
Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions
We evaluate the virial coefficients B_k for k<=10 for hard spheres in
dimensions D=2,...,8. Virial coefficients with k even are found to be negative
when D>=5. This provides strong evidence that the leading singularity for the
virial series lies away from the positive real axis when D>=5. Further analysis
provides evidence that negative virial coefficients will be seen for some k>10
for D=4, and there is a distinct possibility that negative virial coefficients
will also eventually occur for D=3.Comment: 33 pages, 12 figure
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