On the supremal p-negative type of a finite metric space

2011/08/02 by Sanchez, Stephen
#51F99 (Primary) 46B85 #54E35 (Secondary) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1108.0451

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.

Related

• Strict p-negative type of a metric space
• Optimal lower bounds on the maximal p-negative type of finite metric spaces
• Estimating the gap of finite metric spaces of strict p-negative type
• On the gap of finite metric spaces of p-negative type
• Metric graphs of negative type