On dissimilarity vectors of (not necessarily positive) weighted trees

Details On dissimilarity vectors of (not necessarily positive) weighted trees On dissimilarity vectors of (not necessarily positive) weighted trees

2010-04-20

arxiv.org/abs/1004.3406v2

Mathematics

Combinatorics

10 pages, 5 figures

Scientific paper

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 D_{i_1,....,i_k}(T) as the sum 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, 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.

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