Journal of Symbolic Computation vol:44 issue:8 pages:1079-1086
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 in >= 5. Using a computer algebra system, we can prove these conjectures for m = 5. (C) 2009 Elsevier Ltd. All rights reserved.