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.
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Chepoi, V., Fichet, B. A Note on Circular Decomposable Metrics. Geometriae Dedicata 69, 237–240 (1998). https://doi.org/10.1023/A:1004907919611
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DOI: https://doi.org/10.1023/A:1004907919611