InternalInversions on BinaryWord
The pairs i < j with w(i) > w(j) that lie in the same block of the sorted word.
FindStat's St000921. The sorted word is the zeros then the ones, so a pair is internal when both positions are among the first z or both after.
Called as CombinatorialStat(x, "InternalInversions"). The head's page has its examples.
Live
Distribution
Over BinaryWords at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000921
The number of internal inversions of a binary word.
| Object | Value |
|---|---|
0 | 0 |
1 | 0 |
00 | 0 |
01 | 0 |
10 | 0 |
11 | 0 |
000 | 0 |
001 | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000921 has the rest.