Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000712
Mapping
St000712: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 4
[2]
 => 10
[1,1]
 => 6
[3]
 => 20
[2,1]
 => 20
[1,1,1]
 => 4
[4]
 => 35
[3,1]
 => 45
[2,2]
 => 20
[2,1,1]
 => 15
[1,1,1,1]
 => 1
[5]
 => 56
[4,1]
 => 84
[3,2]
 => 60
[3,1,1]
 => 36
[2,2,1]
 => 20
[2,1,1,1]
 => 4
[1,1,1,1,1]
 => 0
[6]
 => 84
[5,1]
 => 140
[4,2]
 => 126
[4,1,1]
 => 70
[3,3]
 => 50
[3,2,1]
 => 64
[3,1,1,1]
 => 10
[2,2,2]
 => 10
[2,2,1,1]
 => 6
[2,1,1,1,1]
 => 0
[1,1,1,1,1,1]
 => 0
[7]
 => 120
[6,1]
 => 216
[5,2]
 => 224
[5,1,1]
 => 120
[4,3]
 => 140
[4,2,1]
 => 140
[4,1,1,1]
 => 20
[3,3,1]
 => 60
[3,2,2]
 => 36
[3,2,1,1]
 => 20
[3,1,1,1,1]
 => 0
[2,2,2,1]
 => 4
[2,2,1,1,1]
 => 0
[2,1,1,1,1,1]
 => 0
[1,1,1,1,1,1,1]
 => 0
[8]
 => 165
[7,1]
 => 315
[6,2]
 => 360
[6,1,1]
 => 189
[5,3]
 => 280
[5,2,1]
 => 256
Description
The number of semistandard Young tableau of given shape, with entries at most 4. This is also the dimension of the corresponding irreducible representation of $GL_4$.