RowRemovalGrundyValue on IntegerPartition
The Grundy value of the game that removes cells from the end of a row while the diagram stays a partition: staircase nim, the nim-sum of the differences of consecutive parts at odd positions.
Called as CombinatorialStat(x, "RowRemovalGrundyValue"). 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 St001055
The Grundy value for the game of removing cells of a row in an integer partition.
| Object | Value |
|---|---|
[] | 0 |
[1] | 1 |
[2] | 2 |
[3] | 3 |
[4] | 4 |
[5] | 5 |
[6] | 6 |
[7] | 7 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001055 has the rest.