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In book "Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne" is written

The Kendall tau distance between two rankings is the number of pairs that are in different order in the two rankings. For example, the Kendall tau distance between 0 3 1 6 2 5 4 and 1 0 3 6 4 2 5 is four because the pairs 0-1, 3-1, 2-4, 5-4 are in different relative order in the two rankings, but all other pairs are in the same relative order.

But what about 6-0, 6-3 and etc, these pairs are in different relative order too. I don't understand this explanation. May anybody explain it well, please?

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  • $\begingroup$ Maybe this question will be closed as duplicate, but I couldn't have found an explanation in others questions. $\endgroup$
    – Vitalii Vitrenko
    Aug 17, 2015 at 14:31

1 Answer 1

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In both of the sequences, 0 is before 6. Thus (6,0) does not increase the Kendall tau distance. Similarly, 3 is always before 6 in the sequences.

Regarding 0-1, 0 is before 1 in the first sequence while 1 is before 0 in the second one. That's why (0,1) is increasing the Kendall tau distance.

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