MinimalInversionsEitherDirection on Permutation
The smaller of the number of inversions and the number of non-inversions.
Inversions of p against those of its reverse.
Called as CombinatorialStat(x, "MinimalInversionsEitherDirection"). The head's page has its examples.
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FindStat St001511
The minimal number of transpositions needed to sort a permutation in either direction.
| Object | Value |
|---|---|
[1] | 0 |
[1,2] | 0 |
[2,1] | 0 |
[1,2,3] | 0 |
[1,3,2] | 1 |
[2,1,3] | 1 |
[2,3,1] | 1 |
[3,1,2] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001511 has the rest.