Tau Kendell distance?

Question

Mathematics

In one book on algorithms it is written

The tau Kendell distance between two arrangements of integers is the number of pairs that are in these arrangements in a different order .

Below is an example

The tau Kendall distance between 0 3 1 6 2 5 4 and 1 0 3 6 4 2 5 is four, since the pairs 0-1,
3-1, 2-4, 5-4 are in different relative order, and all other pairs - in the same relative order.

I do not understand what "in a different relative order" means, and why these particular pairs are chosen?

Answer 1

In the first arrangement, 0 comes before 1 (0, 3, 1...), and in the second - later (1, 0, 3...) Therefore, their "relative order" is different. For pairs 0.3 and 0.6, the order is the same - in both arrangements, 0 comes before 3, and before 6.
"Why were these pairs chosen?" - because the rest of the order is the same.