English

On the relation between weighted trees and tropical Grassmannians

Algebraic Geometry 2009-03-12 v1 Combinatorics

Abstract

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.

Cite

@article{arxiv.0903.2010,
  title  = {On the relation between weighted trees and tropical Grassmannians},
  author = {Filip Cools},
  journal= {arXiv preprint arXiv:0903.2010},
  year   = {2009}
}

Comments

11 pages, to appear in Journal of Symbolic Computation

R2 v1 2026-06-21T12:39:32.304Z