有限度量树的增强负型
Enhanced negative type for finite metric trees
摘要：
已知有限度量树具有严格1-负型。在本文中，我们引入了一个新的家庭的不等式，量化的程度的“严格性”的1-负型不等式的有限度量树。这些“增强的1-负型”不等式足够强，足以暗示任何给定的有限度量树对于包含数字1的开区间中的所有p值都必须具有严格的p-负型。此外，这些开区间可以完全根据确定特定树上的路径度量的边权重的无序分布来表征，并且因此在很大程度上独立于树的内部几何形状。从这些计算中，我们能够提取一个新的非线性技术，以改善某些有限度量空间的最大p-负型的下界。一些病理的例子也被认为是为了强调某些技术要点。
英文摘要：
Finite metric trees are known to have strict 1-negative type. In this paper we introduce a new family of inequalities that quantify the extent of the "strictness" of the 1-negative type inequalities for finite metric trees. These inequalities of "enhanced 1-negative type" are sufficiently strong to imply that any given finite metric tree must have strict p-negative type for all values of p in an open interval that contains the number 1. Moreover, these open intervals can be characterized purely in terms of the unordered distribution of edge weights that determine the path metric on the particular tree, and are therefore largely independent of the tree's internal geometry. From these calculations we are able to extract a new non linear technique for improving lower bounds on the maximal p-negative type of certain finite metric spaces. Some pathological examples are also considered in order to stress certain technical points.
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