Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000712
Mapping
Mp00027: Dyck paths —to partition⟶ Integer partitions
St000712: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => []
 => 1
[1,0,1,0]
 => [1]
 => 4
[1,1,0,0]
 => []
 => 1
[1,0,1,0,1,0]
 => [2,1]
 => 20
[1,0,1,1,0,0]
 => [1,1]
 => 6
[1,1,0,0,1,0]
 => [2]
 => 10
[1,1,0,1,0,0]
 => [1]
 => 4
[1,1,1,0,0,0]
 => []
 => 1
[1,0,1,0,1,0,1,0]
 => [3,2,1]
 => 64
[1,0,1,0,1,1,0,0]
 => [2,2,1]
 => 20
[1,0,1,1,0,0,1,0]
 => [3,1,1]
 => 36
[1,0,1,1,0,1,0,0]
 => [2,1,1]
 => 15
[1,0,1,1,1,0,0,0]
 => [1,1,1]
 => 4
[1,1,0,0,1,0,1,0]
 => [3,2]
 => 60
[1,1,0,0,1,1,0,0]
 => [2,2]
 => 20
[1,1,0,1,0,0,1,0]
 => [3,1]
 => 45
[1,1,0,1,0,1,0,0]
 => [2,1]
 => 20
[1,1,0,1,1,0,0,0]
 => [1,1]
 => 6
[1,1,1,0,0,0,1,0]
 => [3]
 => 20
[1,1,1,0,0,1,0,0]
 => [2]
 => 10
[1,1,1,0,1,0,0,0]
 => [1]
 => 4
[1,1,1,1,0,0,0,0]
 => []
 => 1
[1,0,1,0,1,0,1,0,1,0]
 => [4,3,2,1]
 => 64
[1,0,1,0,1,0,1,1,0,0]
 => [3,3,2,1]
 => 20
[1,0,1,0,1,1,0,0,1,0]
 => [4,2,2,1]
 => 36
[1,0,1,0,1,1,0,1,0,0]
 => [3,2,2,1]
 => 15
[1,0,1,0,1,1,1,0,0,0]
 => [2,2,2,1]
 => 4
[1,0,1,1,0,0,1,0,1,0]
 => [4,3,1,1]
 => 60
[1,0,1,1,0,0,1,1,0,0]
 => [3,3,1,1]
 => 20
[1,0,1,1,0,1,0,0,1,0]
 => [4,2,1,1]
 => 45
[1,0,1,1,0,1,0,1,0,0]
 => [3,2,1,1]
 => 20
[1,0,1,1,0,1,1,0,0,0]
 => [2,2,1,1]
 => 6
[1,0,1,1,1,0,0,0,1,0]
 => [4,1,1,1]
 => 20
[1,0,1,1,1,0,0,1,0,0]
 => [3,1,1,1]
 => 10
[1,0,1,1,1,0,1,0,0,0]
 => [2,1,1,1]
 => 4
[1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1]
 => 1
[1,1,0,0,1,0,1,0,1,0]
 => [4,3,2]
 => 140
[1,1,0,0,1,0,1,1,0,0]
 => [3,3,2]
 => 45
[1,1,0,0,1,1,0,0,1,0]
 => [4,2,2]
 => 84
[1,1,0,0,1,1,0,1,0,0]
 => [3,2,2]
 => 36
[1,1,0,0,1,1,1,0,0,0]
 => [2,2,2]
 => 10
[1,1,0,1,0,0,1,0,1,0]
 => [4,3,1]
 => 175
[1,1,0,1,0,0,1,1,0,0]
 => [3,3,1]
 => 60
[1,1,0,1,0,1,0,0,1,0]
 => [4,2,1]
 => 140
[1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => 64
[1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => 20
[1,1,0,1,1,0,0,0,1,0]
 => [4,1,1]
 => 70
[1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => 36
[1,1,0,1,1,0,1,0,0,0]
 => [2,1,1]
 => 15
[1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => 4
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 $GL_4$.