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The ℓp-function on trees

Authors

  • F. R. McMorris,

    Corresponding author
    1. Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616
    2. Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
    • Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616
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  • Henry Martyn Mulder,

    1. Econometrisch Instituut, Erasmus Universiteit, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands
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  • O. Ortega

    1. Department of Mathematics, Harold Washington College, Chicago, Illinois 60601
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Abstract

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 equation 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

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