BerkovichGarvanRank on IntegerPartition
The sum of a checkerboard filling of the diagram, +1 on cells whose coordinates sum to an even number and -1 on the others.
A row of even length cancels and one of odd length leaves a single cell, counted + in the first row, - in the second, and so on.
Called as CombinatorialStat(x, "BerkovichGarvanRank"). The head's page has its examples.
Live
Distribution
Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.
FindStat St001383
The BG-rank of an integer partition.
| Object | Value |
|---|---|
[1] | 1 |
[2] | 0 |
[3] | 1 |
[4] | 0 |
[5] | 1 |
[6] | 0 |
[7] | 1 |
[8] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001383 has the rest.