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Geometriae Dedicata

, Volume 69, Issue 3, pp 237–240 | Cite as

A Note on Circular Decomposable Metrics

  • Victor Chepoi
  • Bernard Fichet
Article

Abstract

A metric d on a finite set X is called a Kalmanson metric if there exists a circular ordering ζ of points of X, such that d(y, u) + d(z, v) ≥ d(y, z) + d(u, v) for all crossing pairs yu and zv of ζ. We prove that any Kalmanson metric d is an l1-metric, i.e. d can be written as a nonnegative linear combination of split metrics. The splits in the decomposition of d can be selected to form a circular system of splits in the sense of Bandelt and Dress.

l1-metric circular decomposable metric Crofton formula 

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Victor Chepoi
    • 1
  • Bernard Fichet
    • 1
  1. 1.Laboratoire de BiomathématiquesUniversité d'Aix Marseille IIMarseille Cedex 5France

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