LengthCrank on IntegerPartition
The number of parts when λ has no 1s, else (parts larger than the number of 1s) minus (the number of 1s).
Crank has the largest part where this has the number of parts; FindStat's St000146 follows the code, which takes the length.
Called as CombinatorialStat(x, "LengthCrank"). 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 St000146
The Andrews-Garvan crank of a partition.
| Object | Value |
|---|---|
[] | 0 |
[1] | -1 |
[2] | 1 |
[3] | 1 |
[4] | 1 |
[5] | 1 |
[6] | 1 |
[7] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000146 has the rest.