NonInversionSum on BinaryWord
The sum of j - i over the pairs i < j with w(i) < w(j).
FindStat's St000348.
Called as CombinatorialStat(x, "NonInversionSum"). 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.
Also on
The same name on other carriers, each its own implementation: Permutation.
FindStat St000348
The non-inversion sum of a binary word.
| Object | Value |
|---|---|
0 | 0 |
1 | 0 |
00 | 0 |
01 | 1 |
10 | 0 |
11 | 0 |
000 | 0 |
001 | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000348 has the rest.