Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000716
Mapping
St000716: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2]
 => 21
[1,1]
 => 14
[3]
 => 56
[2,1]
 => 64
[1,1,1]
 => 14
[4]
 => 126
[3,1]
 => 189
[2,2]
 => 90
[2,1,1]
 => 70
[1,1,1,1]
 => 0
[5]
 => 252
[4,1]
 => 448
[3,2]
 => 350
[3,1,1]
 => 216
[2,2,1]
 => 126
[2,1,1,1]
 => 0
[1,1,1,1,1]
 => 0
[6]
 => 462
[5,1]
 => 924
[4,2]
 => 924
[4,1,1]
 => 525
[3,3]
 => 385
[3,2,1]
 => 512
[3,1,1,1]
 => 0
[2,2,2]
 => 84
[2,2,1,1]
 => 0
[2,1,1,1,1]
 => 0
[1,1,1,1,1,1]
 => 0
[7]
 => 792
[6,1]
 => 1728
[5,2]
 => 2016
[5,1,1]
 => 1100
[4,3]
 => 1344
[4,2,1]
 => 1386
[4,1,1,1]
 => 0
[3,3,1]
 => 616
[3,2,2]
 => 378
[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]
 => 1287
[7,1]
 => 3003
[6,2]
 => 3900
[6,1,1]
 => 2079
[5,3]
 => 3276
[5,2,1]
 => 3072
[5,1,1,1]
 => 0
Description
The dimension of the irreducible representation of Sp(6) labelled by an integer partition. Consider the symplectic group $Sp(2n)$. Then the integer partition $(\mu_1,\dots,\mu_k)$ of length at most $n$ corresponds to the weight vector $(\mu_1-\mu_2,\dots,\mu_{k-2}-\mu_{k-1},\mu_n,0,\dots,0)$. For example, the integer partition $(2)$ labels the symmetric square of the vector representation, whereas the integer partition $(1,1)$ labels the second fundamental representation.
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: 1% ●values known / values provided: 63%●distinct values known / distinct values provided: 1%
Values
[2]
 => []
 => ?
 => ?
 => ? = 21 + 1
[1,1]
 => [1]
 => []
 => ?
 => ? = 14 + 1
[3]
 => []
 => ?
 => ?
 => ? = 56 + 1
[2,1]
 => [1]
 => []
 => ?
 => ? = 64 + 1
[1,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 14 + 1
[4]
 => []
 => ?
 => ?
 => ? = 126 + 1
[3,1]
 => [1]
 => []
 => ?
 => ? = 189 + 1
[2,2]
 => [2]
 => []
 => ?
 => ? = 90 + 1
[2,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 70 + 1
[1,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[5]
 => []
 => ?
 => ?
 => ? = 252 + 1
[4,1]
 => [1]
 => []
 => ?
 => ? = 448 + 1
[3,2]
 => [2]
 => []
 => ?
 => ? = 350 + 1
[3,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 216 + 1
[2,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 126 + 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]
 => []
 => ?
 => ?
 => ? = 462 + 1
[5,1]
 => [1]
 => []
 => ?
 => ? = 924 + 1
[4,2]
 => [2]
 => []
 => ?
 => ? = 924 + 1
[4,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 525 + 1
[3,3]
 => [3]
 => []
 => ?
 => ? = 385 + 1
[3,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 512 + 1
[3,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[2,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 84 + 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]
 => []
 => ?
 => ?
 => ? = 792 + 1
[6,1]
 => [1]
 => []
 => ?
 => ? = 1728 + 1
[5,2]
 => [2]
 => []
 => ?
 => ? = 2016 + 1
[5,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 1100 + 1
[4,3]
 => [3]
 => []
 => ?
 => ? = 1344 + 1
[4,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 1386 + 1
[4,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[3,3,1]
 => [3,1]
 => [1]
 => []
 => ? = 616 + 1
[3,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 378 + 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]
 => []
 => ?
 => ?
 => ? = 1287 + 1
[7,1]
 => [1]
 => []
 => ?
 => ? = 3003 + 1
[6,2]
 => [2]
 => []
 => ?
 => ? = 3900 + 1
[6,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 2079 + 1
[5,3]
 => [3]
 => []
 => ?
 => ? = 3276 + 1
[5,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 3072 + 1
[5,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[4,4]
 => [4]
 => []
 => ?
 => ? = 1274 + 1
[4,3,1]
 => [3,1]
 => [1]
 => []
 => ? = 2205 + 1
[4,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 1078 + 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]
 => []
 => ? = 594 + 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]
 => []
 => ?
 => ?
 => ? = 2002 + 1
[8,1]
 => [1]
 => []
 => ?
 => ? = 4928 + 1
[7,2]
 => [2]
 => []
 => ?
 => ? = 6930 + 1
[7,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 3640 + 1
[6,3]
 => [3]
 => []
 => ?
 => ? = 6720 + 1
[6,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 6006 + 1
[6,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[5,4]
 => [4]
 => []
 => ?
 => ? = 4116 + 1
[5,3,1]
 => [3,1]
 => [1]
 => []
 => ? = 5460 + 1
[5,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 2464 + 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]
 => []
 => ? = 2184 + 1
[4,3,2]
 => [3,2]
 => [2]
 => []
 => ? = 2240 + 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: 1% ●values known / values provided: 63%●distinct values known / distinct values provided: 1%
Values
[2]
 => []
 => ?
 => ?
 => ? = 21 + 1
[1,1]
 => [1]
 => []
 => ?
 => ? = 14 + 1
[3]
 => []
 => ?
 => ?
 => ? = 56 + 1
[2,1]
 => [1]
 => []
 => ?
 => ? = 64 + 1
[1,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 14 + 1
[4]
 => []
 => ?
 => ?
 => ? = 126 + 1
[3,1]
 => [1]
 => []
 => ?
 => ? = 189 + 1
[2,2]
 => [2]
 => []
 => ?
 => ? = 90 + 1
[2,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 70 + 1
[1,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[5]
 => []
 => ?
 => ?
 => ? = 252 + 1
[4,1]
 => [1]
 => []
 => ?
 => ? = 448 + 1
[3,2]
 => [2]
 => []
 => ?
 => ? = 350 + 1
[3,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 216 + 1
[2,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 126 + 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]
 => []
 => ?
 => ?
 => ? = 462 + 1
[5,1]
 => [1]
 => []
 => ?
 => ? = 924 + 1
[4,2]
 => [2]
 => []
 => ?
 => ? = 924 + 1
[4,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 525 + 1
[3,3]
 => [3]
 => []
 => ?
 => ? = 385 + 1
[3,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 512 + 1
[3,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[2,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 84 + 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]
 => []
 => ?
 => ?
 => ? = 792 + 1
[6,1]
 => [1]
 => []
 => ?
 => ? = 1728 + 1
[5,2]
 => [2]
 => []
 => ?
 => ? = 2016 + 1
[5,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 1100 + 1
[4,3]
 => [3]
 => []
 => ?
 => ? = 1344 + 1
[4,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 1386 + 1
[4,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[3,3,1]
 => [3,1]
 => [1]
 => []
 => ? = 616 + 1
[3,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 378 + 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]
 => []
 => ?
 => ?
 => ? = 1287 + 1
[7,1]
 => [1]
 => []
 => ?
 => ? = 3003 + 1
[6,2]
 => [2]
 => []
 => ?
 => ? = 3900 + 1
[6,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 2079 + 1
[5,3]
 => [3]
 => []
 => ?
 => ? = 3276 + 1
[5,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 3072 + 1
[5,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[4,4]
 => [4]
 => []
 => ?
 => ? = 1274 + 1
[4,3,1]
 => [3,1]
 => [1]
 => []
 => ? = 2205 + 1
[4,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 1078 + 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]
 => []
 => ? = 594 + 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]
 => []
 => ?
 => ?
 => ? = 2002 + 1
[8,1]
 => [1]
 => []
 => ?
 => ? = 4928 + 1
[7,2]
 => [2]
 => []
 => ?
 => ? = 6930 + 1
[7,1,1]
 => [1,1]
 => [1]
 => []
 => ? = 3640 + 1
[6,3]
 => [3]
 => []
 => ?
 => ? = 6720 + 1
[6,2,1]
 => [2,1]
 => [1]
 => []
 => ? = 6006 + 1
[6,1,1,1]
 => [1,1,1]
 => [1,1]
 => [1]
 => 1 = 0 + 1
[5,4]
 => [4]
 => []
 => ?
 => ? = 4116 + 1
[5,3,1]
 => [3,1]
 => [1]
 => []
 => ? = 5460 + 1
[5,2,2]
 => [2,2]
 => [2]
 => []
 => ? = 2464 + 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]
 => []
 => ? = 2184 + 1
[4,3,2]
 => [3,2]
 => [2]
 => []
 => ? = 2240 + 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.