DiagonalArmSum on IntegerPartition
The sum of the arms of the cells on the main diagonal.
FindStat's spin (St000319) counts the crossings of the border strips and its dinv adjustment (St000320) sums over their starting columns; each strip contributes its first part less 1, which is the arm of one diagonal cell, and the two agree on every row.
Called as CombinatorialStat(x, "DiagonalArmSum"). 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 St000319
The spin of an integer partition.
| Object | Value |
|---|---|
[1] | 0 |
[2] | 1 |
[3] | 2 |
[4] | 3 |
[5] | 4 |
[6] | 5 |
[7] | 6 |
[8] | 7 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000319 has the rest.
FindStat St000320
The dinv adjustment of an integer partition.
| Object | Value |
|---|---|
[1] | 0 |
[2] | 1 |
[3] | 2 |
[4] | 3 |
[5] | 4 |
[6] | 5 |
[7] | 6 |
[8] | 7 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000320 has the rest.