Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000813
Mapping
St000813: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2]
 => 1
[1,1]
 => 3
[3]
 => 1
[2,1]
 => 4
[1,1,1]
 => 10
[4]
 => 1
[3,1]
 => 5
[2,2]
 => 9
[2,1,1]
 => 20
[1,1,1,1]
 => 47
[5]
 => 1
[4,1]
 => 6
[3,2]
 => 14
[3,1,1]
 => 30
[2,2,1]
 => 50
[2,1,1,1]
 => 110
[1,1,1,1,1]
 => 246
[6]
 => 1
[5,1]
 => 7
[4,2]
 => 20
[4,1,1]
 => 42
[3,3]
 => 29
[3,2,1]
 => 97
[3,1,1,1]
 => 206
[2,2,2]
 => 157
[2,2,1,1]
 => 338
[2,1,1,1,1]
 => 732
[1,1,1,1,1,1]
 => 1602
[7]
 => 1
[6,1]
 => 8
[5,2]
 => 27
[5,1,1]
 => 56
[4,3]
 => 49
[4,2,1]
 => 159
[4,1,1,1]
 => 332
[3,3,1]
 => 224
[3,2,2]
 => 353
[3,2,1,1]
 => 743
[3,1,1,1,1]
 => 1568
[2,2,2,1]
 => 1184
[2,2,1,1,1]
 => 2513
[2,1,1,1,1,1]
 => 5357
[1,1,1,1,1,1,1]
 => 11481
[8]
 => 1
[7,1]
 => 9
[6,2]
 => 35
[6,1,1]
 => 72
[5,3]
 => 76
[5,2,1]
 => 242
[5,1,1,1]
 => 500
Description
The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. This is also the sum of the entries in the column specified by the partition of the change of basis matrix from elementary symmetric functions to monomial symmetric functions.