The ℓp-function on trees

A p-value of a sequence π = (x1, x2,…, xk) of elements of a finite metric space (X, d) is an element x for which \documentclass{article}\usepackage{mathrsfs}\usepackage{amsmath}\pagestyle{empty}\begin{document}$\sum_{i=1}^{k}d^p(x,x_i)$\end{document} **image** is minimum. The function ℓp with domain the set of all finite sequences defined by ℓp(π) = {x: x is a p-value of π} is called the ℓp-function on X. The ℓp-functions with p = 1 and p = 2 are the well-studied median and mean functions respectively. In this article, the ℓp-function on finite trees is characterized axiomatically. © 2011 Wiley Periodicals, Inc. NETWORKS, 2012 © 2012 Wiley Periodicals, Inc.