Optimal lower bounds on the maximal p-negative type of finite metric spaces

Details Optimal lower bounds on the maximal p-negative type of finite metric spaces Optimal lower bounds on the maximal p-negative type of finite metric spaces

2008-07-17

arxiv.org/abs/0807.2705v1

Mathematics

Functional Analysis

10 pages

Scientific paper

This article derives lower bounds on the supremal (strict) p-negative type of finite metric spaces using purely elementary techniques. The bounds depend only on the cardinality and the (scaled) diameter of the underlying finite metric space. Examples show that these lower bounds can easily be best possible under clearly delineated circumstances. We further point out that the entire theory holds (more generally) for finite semi-metric spaces without modification and wherein the lower bounds are always optimal.

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