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On dissimilarity vectors of (not necessarily positive) weighted trees

Combinatorics 2010-06-29 v2 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.1004.3406,
  title  = {On dissimilarity vectors of (not necessarily positive) weighted trees},
  author = {Elena Rubei},
  journal= {arXiv preprint arXiv:1004.3406},
  year   = {2010}
}

Comments

10 pages, 5 figures