A pairwise mapping is combinatorially similar to an ultrametric exactly when its fibers are coherent, its derived value order is antisymmetric, all triangles are isosceles, and its value set can be embedded like a subset of the real line.
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Combinatorial properties of ultrametrics and generalized ultrametrics
A pairwise mapping is combinatorially similar to an ultrametric exactly when its fibers are coherent, its derived value order is antisymmetric, all triangles are isosceles, and its value set can be embedded like a subset of the real line.