Dissimilarity vectors of trees are contained in the tropical Grassmannian

TL;DR

This paper proves that the set of m-dissimilarity vectors of n-trees is contained within the (m,n)-tropical Grassmannian, addressing a question in tropical geometry and phylogenetics.

Contribution

It establishes a new inclusion relation between dissimilarity vectors of trees and the tropical Grassmannian, generalizing a previous conjecture.

Findings

Proved the inclusion of m-dissimilarity vectors in the tropical Grassmannian

Generalized a conjecture by Cools

Answered a question posed by Pachter and Speyer

Abstract

In this short writing we prove that the set of m-dissimilarity vectors of n-trees is contained in the (m,n)-tropical Grassmannian, answering a question of Pachter and Speyer. We do this by proving a generalization of an equivalent conjecture proposed by Cools.