This is an announcement for the paper "On the supremal $p$-negative type of a finite metric space" by Stephen Sanchez.

Abstract: We study the supremal $p$-negative type of finite metric spaces. An explicit expression for the supremal $p$-negative type $\wp (X,d)$ of a finite metric space $(X,d)$ is given in terms its associated distance matrix, from which the supremal $p$-negative type of the space may be calculated. The method is then used to give a straightforward calculation of the supremal $p$-negative type of the complete bipartite graphs $K_{n,m}$ endowed with the usual path metric. A gap in the spectrum of possible supremal $p$-negative type values of path metric graphs is also proven.

Archive classification: math.FA math.MG

Mathematics Subject Classification: 51F99 (Primary) 46B85, 54E35 (Secondary)

Remarks: 11 pages, 6 figures

Submitted from: stephen.sanchez@unsw.edu.au

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1108.0451

or

http://arXiv.org/abs/1108.0451