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Let T be a (not necessarily positive) weighted tree with n leaves numbered bythe set {1,...,n}. Define the k-weights of the tree D_{i_1,....,i_k}(T) as thesum of the lengths of the edges of the minimal subtree connecting i_1,....,i_k.We will call such numbers "k-weights" of the tree. In this paper, wecharacterize 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.

On dissimilarity vectors of (not necessarily positive) weighted trees