Reconstructing the shape of a tree from observed dissimilarity data
Advances in Applied Mathematics
Arrow's theorem for closed weak hierarchies
Discrete Applied Mathematics
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A collection H of nonempty subsets of a finite set E determines a weak ternary separation relation r(H) on the set E as follows: (a,b,c)@?r(H) if and only if for all clusters A belonging to H, |A@?{a,b,c}|=2 implies that c@?A. We determine conditions on a collection W of set systems of E such that the mapping r that sends each H belonging to W to the weak ternary separation relation r(H) is injective.