On the gap of finite metric spaces of p-negative type

TL;DR

This paper investigates the gap {Gamma} in finite metric spaces of p-negative type, providing formulas to quantify this gap and applying them to specific examples, enhancing understanding of metric space properties.

Contribution

It introduces formulas for calculating the gap {Gamma} in finite p-negative type metric spaces and evaluates this gap for concrete examples, advancing the quantification of negative type properties.

Findings

Formulas for the gap {Gamma} in finite p-negative type spaces

Evaluation of the gap for specific finite metric spaces

Enhanced understanding of the structure of p-negative type spaces

Abstract

Let (X,d) be a metric space of p-negative type. Recently I. Doust and A. Weston introduced a quantification of the p-negative type property, the so called gap {\Gamma} of X. This talk introduces some formulas for the gap {\Gamma} of a finite metric space of strict p-negative type and applies them to evaluate {\Gamma} for some concrete finite metric spaces.