Finite Metric Spaces of Strictly negative Type

Poul G. Hjorth (Invited author)

    Research output: Contribution to conferencePaperResearchpeer-review

    Abstract

    If a finite metric space is of strictly negative type then its transfinite diameter is uniquely realized by an infinite extent (“load vector''). Finite metric spaces that have this property include all trees, and all finite subspaces of Euclidean and Hyperbolic spaces. We prove that if the distance matrix of a finite metric space is both hypermetric and regular, then it is of strictly negative type. We show that the strictly negative type finite subspaces of spheres are precisely those which do not contain two pairs of antipodal points.
    Original languageEnglish
    Publication date2008
    Publication statusPublished - 2008
    EventWorkshop on Distance Geometry - Salzburg, Austria
    Duration: 5 May 20088 May 2008

    Workshop

    WorkshopWorkshop on Distance Geometry
    CountryAustria
    CitySalzburg
    Period05/05/200808/05/2008

    Cite this

    Hjorth, P. G. (2008). Finite Metric Spaces of Strictly negative Type. Paper presented at Workshop on Distance Geometry, Salzburg, Austria.