Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000509
Mapping
St000509: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2]
 => 1
[1,1]
 => -1
[3]
 => 3
[2,1]
 => 0
[1,1,1]
 => -3
[4]
 => 6
[3,1]
 => 2
[2,2]
 => 0
[2,1,1]
 => -2
[1,1,1,1]
 => -6
[5]
 => 10
[4,1]
 => 5
[3,2]
 => 2
[3,1,1]
 => 0
[2,2,1]
 => -2
[2,1,1,1]
 => -5
[1,1,1,1,1]
 => -10
[6]
 => 15
[5,1]
 => 9
[4,2]
 => 5
[4,1,1]
 => 3
[3,3]
 => 3
[3,2,1]
 => 0
[3,1,1,1]
 => -3
[2,2,2]
 => -3
[2,2,1,1]
 => -5
[2,1,1,1,1]
 => -9
[1,1,1,1,1,1]
 => -15
[7]
 => 21
[6,1]
 => 14
[5,2]
 => 9
[5,1,1]
 => 7
[4,3]
 => 6
[4,2,1]
 => 3
[4,1,1,1]
 => 0
[3,3,1]
 => 1
[3,2,2]
 => -1
[3,2,1,1]
 => -3
[3,1,1,1,1]
 => -7
[2,2,2,1]
 => -6
[2,2,1,1,1]
 => -9
[2,1,1,1,1,1]
 => -14
[1,1,1,1,1,1,1]
 => -21
[8]
 => 28
[7,1]
 => 20
[6,2]
 => 14
[6,1,1]
 => 12
[5,3]
 => 10
[5,2,1]
 => 7
[5,1,1,1]
 => 4
Description
The diagonal index (content) of a partition. The '''diagonal index''' of the cell at row $r$ and column $c$ of a partition is $c - r$; this is sometimes called the '''content''' of the cell. The '''diagonal index of a partition''' is the sum of the diagonal index of each cell of the partition.