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arXiv · 2412.18400

On a weighted generalization of Kendall's tau distance

Albert Bruno Piek·Evgeniy Petrov
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Abstract

We introduce a metric on the set of permutations of given order, which is a weighted generalization of Kendall's $\tau$ rank distance and study its properties. Using the edge graph of a permutohedron, we give a criterion which guarantees that a permutation lies metrically between another two fixed permutations. In addition, the conditions under which four points from the resulting metric space form a pseudolinear quadruple were found.

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Albert Bruno Piek, Evgeniy Petrov. 2024-12-24. On a weighted generalization of Kendall's tau distance. https://doi.org/10.1007/s00026-020-00519-y

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