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.

中文翻译：

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关于Kendall的Tau距离的加权推广。

我们在给定阶数的排列集上引入度量，这是Kendall的\（\ tau \）秩距离的加权归纳，并研究其属性。使用置换体的边缘图，我们给出了一个标准，该准则可确保置换在度量上位于另外两个固定置换之间。另外，找到了从所得度量空间中的四个点形成伪线性四元组的条件。