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The ℓ p ‐function on trees
Author(s) -
McMorris F. R.,
Mulder Henry Martyn,
Ortega O.
Publication year - 2012
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.20463
Subject(s) - combinatorics , function (biology) , sequence (biology) , mathematics , domain (mathematical analysis) , metric space , space (punctuation) , metric (unit) , finite set , value (mathematics) , physics , discrete mathematics , mathematical analysis , computer science , chemistry , statistics , biochemistry , operations management , economics , operating system , evolutionary biology , biology
A p ‐value of a sequence π = ( x 1 , x 2 ,…, x k ) 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} is minimum. The function ℓ p with domain the set of all finite sequences defined by ℓ p (π) = { x : x is a p ‐value of π} is called the ℓ p ‐function on X . The ℓ p ‐functions with p = 1 and p = 2 are the well‐studied median and mean functions respectively. In this article, the ℓ p ‐function on finite trees is characterized axiomatically. © 2011 Wiley Periodicals, Inc. NETWORKS, 2012