On a Weighted Generalization of Kendall’s Tau Distance

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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Acknowledgements

The authors thank the anonymous referees for their remarks which considerably improved this article.

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Correspondence to Evgeniy Petrov.

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Evgeniy Petrov was supported by H2020-MSCA-RISE-2014, Project number 645672 (AMMODIT: “Approximation Methods for Molecular Modelling and Diagnosis Tools”).

Communicated by Kolja Knauer

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Piek, A.B., Petrov, E. On a Weighted Generalization of Kendall’s Tau Distance. Ann. Comb. (2021). https://doi.org/10.1007/s00026-020-00519-y

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Keywords

  • Kendall’s tau distance
  • Metric space
  • Permutation
  • Permutohedron

Mathematics Subject Classification

  • 54E35
  • 05A05
  • 05C35