A finite metric tree is a finite connected graph that has no cycles, endowed with an edge weighted path metric. Finite metric trees are known to have strict 1-negative type. In this paper we introduce a new family of inequalities (1) that encode the best possible quantification of the strictness of the non trivial 1-negative type inequalities for finite metric trees. These inequalities are sufficiently strong to imply that any given finite metric tree (T, d) must have strict p-negative type for… CONTINUE READING

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