StandardizedBiAlternatingInversionNumber on Permutation
Half of floor(n/2)^2 plus the signed inversions, each pair i < j weighted by (-1)^(i+j).
Half of the sum of (-1)^(i+j) sgn(p(j) - p(i)) over i < j, shifted by floor(n/2)^2.
Called as CombinatorialStat(x, "StandardizedBiAlternatingInversionNumber"). The head's page has its examples.
Live
Distribution
Over SymmetricGroup at each size, tallied here in your browser; sizes past 8 are not offered.
FindStat St000677
The standardized bi-alternating inversion number of a permutation.
| Object | Value |
|---|---|
[1,2] | 0 |
[2,1] | 1 |
[1,2,3] | 0 |
[1,3,2] | 1 |
[2,1,3] | 1 |
[2,3,1] | 0 |
[3,1,2] | 0 |
[3,2,1] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000677 has the rest.