Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000284
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Mapping
St000284: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2]
 => 1
[1,1]
 => 1
[3]
 => 1
[2,1]
 => 4
[1,1,1]
 => 1
[4]
 => 1
[3,1]
 => 9
[2,2]
 => 4
[2,1,1]
 => 9
[1,1,1,1]
 => 1
[5]
 => 1
[4,1]
 => 16
[3,2]
 => 25
[3,1,1]
 => 36
[2,2,1]
 => 25
[2,1,1,1]
 => 16
[1,1,1,1,1]
 => 1
[6]
 => 1
[5,1]
 => 25
[4,2]
 => 81
[4,1,1]
 => 100
[3,3]
 => 25
[3,2,1]
 => 256
[3,1,1,1]
 => 100
[2,2,2]
 => 25
[2,2,1,1]
 => 81
[2,1,1,1,1]
 => 25
[1,1,1,1,1,1]
 => 1
[7]
 => 1
[6,1]
 => 36
[5,2]
 => 196
[5,1,1]
 => 225
[4,3]
 => 196
[4,2,1]
 => 1225
[4,1,1,1]
 => 400
[3,3,1]
 => 441
[3,2,2]
 => 441
[3,2,1,1]
 => 1225
[3,1,1,1,1]
 => 225
[2,2,2,1]
 => 196
[2,2,1,1,1]
 => 196
[2,1,1,1,1,1]
 => 36
[1,1,1,1,1,1,1]
 => 1
[8]
 => 1
[7,1]
 => 49
[6,2]
 => 400
[6,1,1]
 => 441
[5,3]
 => 784
[5,2,1]
 => 4096
[5,1,1,1]
 => 1225
Description
The Plancherel distribution on integer partitions. This is defined as the distribution induced by the RSK shape of the uniform distribution on permutations. In other words, this is the size of the preimage of the map 'Robinson-Schensted tableau shape' from permutations to integer partitions. Equivalently, this is given by the square of the number of standard Young tableaux of the given shape.