Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000715
Mapping
St000715: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 3
[2]
 => 6
[1,1]
 => 3
[3]
 => 10
[2,1]
 => 8
[1,1,1]
 => 1
[4]
 => 15
[3,1]
 => 15
[2,2]
 => 6
[2,1,1]
 => 3
[1,1,1,1]
 => 0
[5]
 => 21
[4,1]
 => 24
[3,2]
 => 15
[3,1,1]
 => 6
[2,2,1]
 => 3
[2,1,1,1]
 => 0
[1,1,1,1,1]
 => 0
[6]
 => 28
[5,1]
 => 35
[4,2]
 => 27
[4,1,1]
 => 10
[3,3]
 => 10
[3,2,1]
 => 8
[3,1,1,1]
 => 0
[2,2,2]
 => 1
[2,2,1,1]
 => 0
[2,1,1,1,1]
 => 0
[1,1,1,1,1,1]
 => 0
[7]
 => 36
[6,1]
 => 48
[5,2]
 => 42
[5,1,1]
 => 15
[4,3]
 => 24
[4,2,1]
 => 15
[4,1,1,1]
 => 0
[3,3,1]
 => 6
[3,2,2]
 => 3
[3,2,1,1]
 => 0
[3,1,1,1,1]
 => 0
[2,2,2,1]
 => 0
[2,2,1,1,1]
 => 0
[2,1,1,1,1,1]
 => 0
[1,1,1,1,1,1,1]
 => 0
[8]
 => 45
[7,1]
 => 63
[6,2]
 => 60
[6,1,1]
 => 21
[5,3]
 => 42
[5,2,1]
 => 24
Description
The number of semistandard Young tableaux of given shape and entries at most 3. This is also the dimension of the corresponding irreducible representation of $GL_3$.
Matching statistic: St000781
Mapping
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000781: Integer partitions ⟶ ℤResult quality: 3% ●values known / values provided: 65%●distinct values known / distinct values provided: 3%
Values
[1]
 => []
 => ?
 => ?
 => ? = 3 + 1
[2]
 => []
 => ?
 => ?
 => ? = 6 + 1
[1,1]
 => [1]
 => []
 => ?
 => ? = 3 + 1
[3]
 => []
 => ?
 => ?
 => ? = 10 + 1
[2,1]
 => [1]
 => []
 => ?
 => ? = 8 + 1
[1,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 1 + 1
[4]
 => []
 => ?
 => ?
 => ? = 15 + 1
[3,1]
 => [1]
 => []
 => ?
 => ? = 15 + 1
[2,2]
 => [2]
 => []
 => ?
 => ? = 6 + 1
[2,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 3 + 1
[1,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[5]
 => []
 => ?
 => ?
 => ? = 21 + 1
[4,1]
 => [1]
 => []
 => ?
 => ? = 24 + 1
[3,2]
 => [2]
 => []
 => ?
 => ? = 15 + 1
[3,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 6 + 1
[2,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 3 + 1
[2,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[6]
 => []
 => ?
 => ?
 => ? = 28 + 1
[5,1]
 => [1]
 => []
 => ?
 => ? = 35 + 1
[4,2]
 => [2]
 => []
 => ?
 => ? = 27 + 1
[4,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 10 + 1
[3,3]
 => [3]
 => []
 => ?
 => ? = 10 + 1
[3,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 8 + 1
[3,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[2,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 1 + 1
[2,2,1,1]
 => [2,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 0 + 1
[7]
 => []
 => ?
 => ?
 => ? = 36 + 1
[6,1]
 => [1]
 => []
 => ?
 => ? = 48 + 1
[5,2]
 => [2]
 => []
 => ?
 => ? = 42 + 1
[5,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 15 + 1
[4,3]
 => [3]
 => []
 => ?
 => ? = 24 + 1
[4,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 15 + 1
[4,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[3,3,1]
 => [3,1]
 => [1]
 => []
 => ? = 6 + 1
[3,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 3 + 1
[3,2,1,1]
 => [2,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[3,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[2,2,2,1]
 => [2,2,1]
 => [2,1]
 => [1]
 => 1 = 0 + 1
[2,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[2,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 0 + 1
[1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1 = 0 + 1
[8]
 => []
 => ?
 => ?
 => ? = 45 + 1
[7,1]
 => [1]
 => []
 => ?
 => ? = 63 + 1
[6,2]
 => [2]
 => []
 => ?
 => ? = 60 + 1
[6,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 21 + 1
[5,3]
 => [3]
 => []
 => ?
 => ? = 42 + 1
[5,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 24 + 1
[5,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[4,4]
 => [4]
 => []
 => ?
 => ? = 15 + 1
[4,3,1]
 => [3,1]
 => [1]
 => []
 => ? = 15 + 1
[4,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 6 + 1
[4,2,1,1]
 => [2,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[4,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[3,3,2]
 => [3,2]
 => [2]
 => []
 => ? = 3 + 1
[3,3,1,1]
 => [3,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[3,2,2,1]
 => [2,2,1]
 => [2,1]
 => [1]
 => 1 = 0 + 1
[3,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[3,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 0 + 1
[2,2,2,2]
 => [2,2,2]
 => [2,2]
 => [2]
 => 1 = 0 + 1
[2,2,2,1,1]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1 = 0 + 1
[2,2,1,1,1,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 0 + 1
[2,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1 = 0 + 1
[1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1 = 0 + 1
[9]
 => []
 => ?
 => ?
 => ? = 55 + 1
[8,1]
 => [1]
 => []
 => ?
 => ? = 80 + 1
[7,2]
 => [2]
 => []
 => ?
 => ? = 81 + 1
[7,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 28 + 1
[6,3]
 => [3]
 => []
 => ?
 => ? = 64 + 1
[6,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 35 + 1
[6,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[5,4]
 => [4]
 => []
 => ?
 => ? = 35 + 1
[5,3,1]
 => [3,1]
 => [1]
 => []
 => ? = 27 + 1
[5,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 10 + 1
[5,2,1,1]
 => [2,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[5,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[4,4,1]
 => [4,1]
 => [1]
 => []
 => ? = 10 + 1
[4,3,1,1]
 => [3,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[4,2,2,1]
 => [2,2,1]
 => [2,1]
 => [1]
 => 1 = 0 + 1
[4,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[4,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 0 + 1
[3,3,2,1]
 => [3,2,1]
 => [2,1]
 => [1]
 => 1 = 0 + 1
[3,3,1,1,1]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[3,2,2,2]
 => [2,2,2]
 => [2,2]
 => [2]
 => 1 = 0 + 1
[3,2,2,1,1]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1 = 0 + 1
[3,2,1,1,1,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 0 + 1
[3,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1 = 0 + 1
[2,2,2,2,1]
 => [2,2,2,1]
 => [2,2,1]
 => [2,1]
 => 1 = 0 + 1
[2,2,2,1,1,1]
 => [2,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 1 = 0 + 1
[2,2,1,1,1,1,1]
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1 = 0 + 1
[2,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1 = 0 + 1
[1,1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 1 = 0 + 1
[7,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[6,2,1,1]
 => [2,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[6,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[5,3,1,1]
 => [3,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[5,2,2,1]
 => [2,2,1]
 => [2,1]
 => [1]
 => 1 = 0 + 1
[5,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
Description
The number of proper colouring schemes of a Ferrers diagram. A colouring of a Ferrers diagram is proper if no two cells in a row or in a column have the same colour. The minimal number of colours needed is the maximum of the length and the first part of the partition, because we can restrict a latin square to the shape. We can associate to each colouring the integer partition recording how often each colour is used, see [1]. This statistic is the number of distinct such integer partitions that occur.
Matching statistic: St001901
Mapping
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001901: Integer partitions ⟶ ℤResult quality: 3% ●values known / values provided: 65%●distinct values known / distinct values provided: 3%
Values
[1]
 => []
 => ?
 => ?
 => ? = 3 + 1
[2]
 => []
 => ?
 => ?
 => ? = 6 + 1
[1,1]
 => [1]
 => []
 => ?
 => ? = 3 + 1
[3]
 => []
 => ?
 => ?
 => ? = 10 + 1
[2,1]
 => [1]
 => []
 => ?
 => ? = 8 + 1
[1,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 1 + 1
[4]
 => []
 => ?
 => ?
 => ? = 15 + 1
[3,1]
 => [1]
 => []
 => ?
 => ? = 15 + 1
[2,2]
 => [2]
 => []
 => ?
 => ? = 6 + 1
[2,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 3 + 1
[1,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[5]
 => []
 => ?
 => ?
 => ? = 21 + 1
[4,1]
 => [1]
 => []
 => ?
 => ? = 24 + 1
[3,2]
 => [2]
 => []
 => ?
 => ? = 15 + 1
[3,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 6 + 1
[2,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 3 + 1
[2,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[6]
 => []
 => ?
 => ?
 => ? = 28 + 1
[5,1]
 => [1]
 => []
 => ?
 => ? = 35 + 1
[4,2]
 => [2]
 => []
 => ?
 => ? = 27 + 1
[4,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 10 + 1
[3,3]
 => [3]
 => []
 => ?
 => ? = 10 + 1
[3,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 8 + 1
[3,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[2,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 1 + 1
[2,2,1,1]
 => [2,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 0 + 1
[7]
 => []
 => ?
 => ?
 => ? = 36 + 1
[6,1]
 => [1]
 => []
 => ?
 => ? = 48 + 1
[5,2]
 => [2]
 => []
 => ?
 => ? = 42 + 1
[5,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 15 + 1
[4,3]
 => [3]
 => []
 => ?
 => ? = 24 + 1
[4,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 15 + 1
[4,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[3,3,1]
 => [3,1]
 => [1]
 => []
 => ? = 6 + 1
[3,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 3 + 1
[3,2,1,1]
 => [2,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[3,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[2,2,2,1]
 => [2,2,1]
 => [2,1]
 => [1]
 => 1 = 0 + 1
[2,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[2,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 0 + 1
[1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1 = 0 + 1
[8]
 => []
 => ?
 => ?
 => ? = 45 + 1
[7,1]
 => [1]
 => []
 => ?
 => ? = 63 + 1
[6,2]
 => [2]
 => []
 => ?
 => ? = 60 + 1
[6,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 21 + 1
[5,3]
 => [3]
 => []
 => ?
 => ? = 42 + 1
[5,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 24 + 1
[5,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[4,4]
 => [4]
 => []
 => ?
 => ? = 15 + 1
[4,3,1]
 => [3,1]
 => [1]
 => []
 => ? = 15 + 1
[4,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 6 + 1
[4,2,1,1]
 => [2,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[4,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[3,3,2]
 => [3,2]
 => [2]
 => []
 => ? = 3 + 1
[3,3,1,1]
 => [3,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[3,2,2,1]
 => [2,2,1]
 => [2,1]
 => [1]
 => 1 = 0 + 1
[3,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[3,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 0 + 1
[2,2,2,2]
 => [2,2,2]
 => [2,2]
 => [2]
 => 1 = 0 + 1
[2,2,2,1,1]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1 = 0 + 1
[2,2,1,1,1,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 0 + 1
[2,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1 = 0 + 1
[1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1 = 0 + 1
[9]
 => []
 => ?
 => ?
 => ? = 55 + 1
[8,1]
 => [1]
 => []
 => ?
 => ? = 80 + 1
[7,2]
 => [2]
 => []
 => ?
 => ? = 81 + 1
[7,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 28 + 1
[6,3]
 => [3]
 => []
 => ?
 => ? = 64 + 1
[6,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 35 + 1
[6,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[5,4]
 => [4]
 => []
 => ?
 => ? = 35 + 1
[5,3,1]
 => [3,1]
 => [1]
 => []
 => ? = 27 + 1
[5,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 10 + 1
[5,2,1,1]
 => [2,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[5,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[4,4,1]
 => [4,1]
 => [1]
 => []
 => ? = 10 + 1
[4,3,1,1]
 => [3,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[4,2,2,1]
 => [2,2,1]
 => [2,1]
 => [1]
 => 1 = 0 + 1
[4,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[4,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 0 + 1
[3,3,2,1]
 => [3,2,1]
 => [2,1]
 => [1]
 => 1 = 0 + 1
[3,3,1,1,1]
 => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[3,2,2,2]
 => [2,2,2]
 => [2,2]
 => [2]
 => 1 = 0 + 1
[3,2,2,1,1]
 => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1 = 0 + 1
[3,2,1,1,1,1]
 => [2,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => 1 = 0 + 1
[3,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1 = 0 + 1
[2,2,2,2,1]
 => [2,2,2,1]
 => [2,2,1]
 => [2,1]
 => 1 = 0 + 1
[2,2,2,1,1,1]
 => [2,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 1 = 0 + 1
[2,2,1,1,1,1,1]
 => [2,1,1,1,1,1]
 => [1,1,1,1,1]
 => [1,1,1,1]
 => 1 = 0 + 1
[2,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => [1,1,1,1,1]
 => 1 = 0 + 1
[1,1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1,1]
 => [1,1,1,1,1,1,1]
 => [1,1,1,1,1,1]
 => 1 = 0 + 1
[7,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[6,2,1,1]
 => [2,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[6,1,1,1,1]
 => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[5,3,1,1]
 => [3,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[5,2,2,1]
 => [2,2,1]
 => [2,1]
 => [1]
 => 1 = 0 + 1
[5,2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
Description
The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition.