On dissimilarity vectors of (not necessarily positive) weighted trees

الأصل · EN

Let T be a (not necessarily positive) weighted tree with n leaves numbered by the set 1,...,n. Define the k-weights of the tree Dᵢ₁,....,ᵢₖ(T) as the sum of the lengths of the edges of the minimal subtree connecting i₁,....,iₖ. We will call such numbers "k-weights" of the tree. In this paper, we characterize the sets of real numbers indexed by the subsets of any cardinality >= 2 of a n-set to be the weights of a tree with n leaves.