On the relation between weighted trees and tropical Grassmannians

2009/03/11 by Filip Cools, Cools, Filip
Computer Science · Mathematics · #05C05 #05C12 #14M15 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation #math.AG #math.CO #msc:05C05 #msc:05C12 #msc:14M15

paper · pdf · doi:10.48550/arxiv.0903.2010

11 pages, to appear in Journal of Symbolic Computation

arxiv created 2009/03/11 · openalex publication_date 2009/03/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Dissimilarity vectors of trees are contained in the tropical Grassmannian
• A tropical interpretation of m-dissimilarity maps
• The Tropical Grassmannian
• Tropical Grassmannian and Tropical Linear Varieties from phylogenetic trees
• Tropicalization of Positive Grassmannians