Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001599
Mapping
St001599: 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]
 => 2
[2,1]
 => 3
[1,1,1]
 => 1
[4]
 => 4
[3,1]
 => 9
[2,2]
 => 5
[2,1,1]
 => 7
[1,1,1,1]
 => 2
[5]
 => 9
[4,1]
 => 26
[3,2]
 => 28
[3,1,1]
 => 30
[2,2,1]
 => 24
[2,1,1,1]
 => 17
[1,1,1,1,1]
 => 4
[6]
 => 20
[5,1]
 => 75
[4,2]
 => 114
[4,1,1]
 => 117
[3,3]
 => 59
[3,2,1]
 => 170
[3,1,1,1]
 => 96
[2,2,2]
 => 49
[2,2,1,1]
 => 83
[2,1,1,1,1]
 => 42
[1,1,1,1,1,1]
 => 8
[7]
 => 48
[6,1]
 => 214
[5,2]
 => 421
[5,1,1]
 => 419
[4,3]
 => 382
[4,2,1]
 => 874
[4,1,1,1]
 => 459
[3,3,1]
 => 493
[3,2,2]
 => 474
[3,2,1,1]
 => 745
[3,1,1,1,1]
 => 294
[2,2,2,1]
 => 281
[2,2,1,1,1]
 => 261
[2,1,1,1,1,1]
 => 104
[1,1,1,1,1,1,1]
 => 16
[8]
 => 115
[7,1]
 => 612
[6,2]
 => 1462
[6,1,1]
 => 1446
[5,3]
 => 1833
[5,2,1]
 => 3875
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees.