Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001908
Mapping
St001908: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 1
[1,1]
 => 1
[3]
 => 1
[2,1]
 => 2
[1,1,1]
 => 1
[4]
 => 1
[3,1]
 => 3
[2,2]
 => 1
[2,1,1]
 => 3
[1,1,1,1]
 => 1
[5]
 => 1
[4,1]
 => 4
[3,2]
 => 2
[3,1,1]
 => 6
[2,2,1]
 => 3
[2,1,1,1]
 => 4
[1,1,1,1,1]
 => 1
[6]
 => 1
[5,1]
 => 5
[4,2]
 => 3
[4,1,1]
 => 10
[3,3]
 => 1
[3,2,1]
 => 7
[3,1,1,1]
 => 10
[2,2,2]
 => 1
[2,2,1,1]
 => 6
[2,1,1,1,1]
 => 5
[1,1,1,1,1,1]
 => 1
[7]
 => 1
[6,1]
 => 6
[5,2]
 => 4
[5,1,1]
 => 15
[4,3]
 => 2
[4,2,1]
 => 12
[4,1,1,1]
 => 20
[3,3,1]
 => 6
[3,2,2]
 => 3
[3,2,1,1]
 => 16
[3,1,1,1,1]
 => 15
[2,2,2,1]
 => 4
[2,2,1,1,1]
 => 10
[2,1,1,1,1,1]
 => 6
[1,1,1,1,1,1,1]
 => 1
[8]
 => 1
[7,1]
 => 7
[6,2]
 => 5
[6,1,1]
 => 21
[5,3]
 => 3
[5,2,1]
 => 18
Description
The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. For example, there are eight tableaux of shape $[3,2,1]$ with maximal entry $3$, but two of them have the same weight.