On the relation between weighted trees and tropical Grassmannians
Abstract
Description
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.
11 pages, to appear in Journal of Symbolic Computation
11 pages, to appear in Journal of Symbolic Computation