Crank on IntegerPartition
The Andrews-Garvan crank: the largest part when λ has no 1s, else (parts larger than the number of 1s) minus (the number of 1s).
Called as CombinatorialStat(x, "Crank"). 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 St000474
Dyson's crank of a partition.
| Object | Value |
|---|---|
[1] | -1 |
[2] | 2 |
[3] | 3 |
[4] | 4 |
[5] | 5 |
[6] | 6 |
[7] | 7 |
[8] | 8 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000474 has the rest.