On the relation between weighted trees and tropical Grassmannians

Details On the relation between weighted trees and tropical Grassmannians On the relation between weighted trees and tropical Grassmannians

2009-03-11

arxiv.org/abs/0903.2010v1

Mathematics

Algebraic Geometry

11 pages, to appear in Journal of Symbolic Computation

Scientific paper

In this article, we will prove that the set of 4-dissimilarity vectors of
n-trees is contained in the tropical Grassmannian G_{4,n}. We will also propose
three equivalent conjectures related to the set of m-dissimilarity vectors of
n-trees for the case m > 4. Using a computer algebra system, we can prove these
conjectures for m = 5.

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