ACBX

In the first case we have abcx with a < b < c and b > x (because [tau] avoids 132), and we can make the transformations abcx [right arrow] acbx [right arrow] axbc, arriving at a permutation with two fewer inversions.

In the first case we have abcx with a < b < c and b > x ([tau] avoids 132), and we can make the transformations abcx [right arrow] acbx [right arrow] axbc, arriving at a permutation with two fewer inversions.