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 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.

arXiv comment8 pages, 1 figure, example added and errors corrected