DiagonalInversions on IntegerPartition

Cells whose arm minus leg is 0 or 1.

On IntegerPartition

Called as CombinatorialStat(x, "DiagonalInversions"). The head's page has its examples.

Live

FindStat St000378

The diagonal inversion number of an integer partition.

Object	Value
[]	0
[1]	1
[2]	2
[3]	2
[4]	2
[5]	2
[6]	2
[7]	2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000378 has the rest.