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Given a family of real numbers parametrized by the $k$-subsets of $\\{1,..., n\\}$, $\\{D_I\\}_{I \\in {\\{1,...,n\\} \\choose k}}$, we say that a weighted tree ${\\cal T}=(T,w)$ with leaves $1,..., n$ realizes the family if $D_I({\\cal T})=D_I$ for any $ I $. 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