Dissimilarity Vectors of Trees are Contained in the Tropical Grassmannian

Abstract

In this short writing, we prove that the set of $m$-dissimilarity vectors of phylogenetic $n$-trees is contained in the tropical Grassmannian ${\cal G}_{m,n}$, answering a question of Pachter and Speyer. We do this by proving an equivalent conjecture proposed by Cools.