Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000815
Mapping
St000815: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2]
 => 2
[1,1]
 => 1
[3]
 => 3
[2,1]
 => 3
[1,1,1]
 => 1
[4]
 => 5
[3,1]
 => 7
[2,2]
 => 4
[2,1,1]
 => 4
[1,1,1,1]
 => 1
[5]
 => 7
[4,1]
 => 13
[3,2]
 => 12
[3,1,1]
 => 11
[2,2,1]
 => 8
[2,1,1,1]
 => 5
[1,1,1,1,1]
 => 1
[6]
 => 11
[5,1]
 => 24
[4,2]
 => 30
[4,1,1]
 => 25
[3,3]
 => 14
[3,2,1]
 => 33
[3,1,1,1]
 => 16
[2,2,2]
 => 9
[2,2,1,1]
 => 13
[2,1,1,1,1]
 => 6
[1,1,1,1,1,1]
 => 1
[7]
 => 15
[6,1]
 => 39
[5,2]
 => 59
[5,1,1]
 => 50
[4,3]
 => 47
[4,2,1]
 => 90
[4,1,1,1]
 => 41
[3,3,1]
 => 48
[3,2,2]
 => 43
[3,2,1,1]
 => 62
[3,1,1,1,1]
 => 22
[2,2,2,1]
 => 22
[2,2,1,1,1]
 => 19
[2,1,1,1,1,1]
 => 7
[1,1,1,1,1,1,1]
 => 1
[8]
 => 22
[7,1]
 => 64
[6,2]
 => 113
[6,1,1]
 => 94
[5,3]
 => 119
[5,2,1]
 => 211
[5,1,1,1]
 => 92
Description
The number of semistandard Young tableaux of partition weight of given shape. The weight of a semistandard Young tableaux is the sequence $(m_1, m_2,\dots)$, where $m_i$ is the number of occurrences of the number $i$ in the tableau. This statistic counts those tableaux whose weight is a weakly decreasing sequence. Alternatively, this is the sum of the entries in the column specified by the partition of the change of basis matrix from Schur functions to monomial symmetric functions.