@**article**{RISC2380,author = {P. Hjorth and P. Lisonek and S. Markvorsen and C. Thomassen},

title = {{Finite metric spaces of strictly negative type}},

language = {english},

abstract = {We prove that, if a finite metric space is of strictly negative type,
then its transfinite diameter is uniquely realized by the infinite extender
(``load vector''). Finite metric spaces that have this property include
all spaces on 2, 3 or 4 points, all trees, and all finite subspaces
of Euclidean spaces. We prove that, if the distance matrix 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.
In connection with an open problem raised by Kelly, we conjecture
that all finite subspaces of hyperbolic spaces are hypermetric and regular,
and hence of strictly negative type.},

journal = {Linear Algebra Appl.},

volume = {270},

pages = {255--273},

isbn_issn = {ISSN 0024-3795},

year = {1998},

refereed = {yes},

length = {19}

}