Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000944
Mapping
St000944: 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]
 => 1
[2,1]
 => 1
[1,1,1]
 => 0
[4]
 => 1
[3,1]
 => 0
[2,2]
 => 1
[2,1,1]
 => 0
[1,1,1,1]
 => 0
[5]
 => 1
[4,1]
 => 4
[3,2]
 => 1
[3,1,1]
 => 0
[2,2,1]
 => 4
[2,1,1,1]
 => 0
[1,1,1,1,1]
 => 0
[6]
 => 2
[5,1]
 => 9
[4,2]
 => 0
[4,1,1]
 => 16
[3,3]
 => 6
[3,2,1]
 => 16
[3,1,1,1]
 => 4
[2,2,2]
 => 4
[2,2,1,1]
 => 0
[2,1,1,1,1]
 => 1
[1,1,1,1,1,1]
 => 0
[7]
 => 2
[6,1]
 => 6
[5,2]
 => 27
[5,1,1]
 => 15
[4,3]
 => 15
[4,2,1]
 => 42
[4,1,1,1]
 => 20
[3,3,1]
 => 6
[3,2,2]
 => 15
[3,2,1,1]
 => 28
[3,1,1,1,1]
 => 0
[2,2,2,1]
 => 13
[2,2,1,1,1]
 => 1
[2,1,1,1,1,1]
 => 0
[1,1,1,1,1,1,1]
 => 0
[8]
 => 2
[7,1]
 => 14
[6,2]
 => 33
[6,1,1]
 => 21
[5,3]
 => 56
[5,2,1]
 => 99
Description
The 3-degree of an integer partition. For an integer partition $\lambda$, this is given by the exponent of 3 in the Gram determinant of the integal Specht module of the symmetric group indexed by $\lambda$. This stupid comment should not be accepted as an edit!