Abstract of a paper by Stephen Sanchez
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
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alspach@math.okstate.edu