Processing math: 100%

Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001178
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Mapping
St001178: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 0
[2]
 => 0
[1,1]
 => 0
[3]
 => 0
[2,1]
 => 3
[1,1,1]
 => 0
[4]
 => 0
[3,1]
 => 8
[2,2]
 => 12
[2,1,1]
 => 8
[1,1,1,1]
 => 0
[5]
 => 0
[4,1]
 => 15
[3,2]
 => 24
[3,1,1]
 => 20
[2,2,1]
 => 24
[2,1,1,1]
 => 15
[1,1,1,1,1]
 => 0
[6]
 => 0
[5,1]
 => 24
[4,2]
 => 40
[4,1,1]
 => 36
[3,3]
 => 48
[3,2,1]
 => 45
[3,1,1,1]
 => 36
[2,2,2]
 => 48
[2,2,1,1]
 => 40
[2,1,1,1,1]
 => 24
[1,1,1,1,1,1]
 => 0
[7]
 => 0
[6,1]
 => 35
[5,2]
 => 60
[5,1,1]
 => 56
[4,3]
 => 75
[4,2,1]
 => 72
[4,1,1,1]
 => 63
[3,3,1]
 => 80
[3,2,2]
 => 80
[3,2,1,1]
 => 72
[3,1,1,1,1]
 => 56
[2,2,2,1]
 => 75
[2,2,1,1,1]
 => 60
[2,1,1,1,1,1]
 => 35
[1,1,1,1,1,1,1]
 => 0
[8]
 => 0
[7,1]
 => 48
[6,2]
 => 84
[6,1,1]
 => 80
[5,3]
 => 108
[5,2,1]
 => 105
Description
Twelve times the variance of the major index among all standard Young tableaux of a partition. For a partition λ of n, this variance is given in [1, Proposition 3.2] by 112(n∑k=1i2−∑i,j∈λh2ij), where the second sum ranges over all cells in λ and hij is the hook length of the cell (i,j)∈λ.