Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001602
Mapping
St001602: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 3
[1,1]
 => 1
[3]
 => 7
[2,1]
 => 8
[1,1,1]
 => 4
[4]
 => 19
[3,1]
 => 33
[2,2]
 => 24
[2,1,1]
 => 27
[1,1,1,1]
 => 9
[5]
 => 47
[4,1]
 => 128
[3,2]
 => 141
[3,1,1]
 => 151
[2,2,1]
 => 119
[2,1,1,1]
 => 85
[1,1,1,1,1]
 => 20
[6]
 => 130
[5,1]
 => 441
[4,2]
 => 699
[4,1,1]
 => 695
[3,3]
 => 344
[3,2,1]
 => 1016
[3,1,1,1]
 => 587
[2,2,2]
 => 309
[2,2,1,1]
 => 486
[2,1,1,1,1]
 => 254
[1,1,1,1,1,1]
 => 45
[7]
 => 343
[6,1]
 => 1495
[5,2]
 => 2952
[5,1,1]
 => 2931
[4,3]
 => 2674
[4,2,1]
 => 6113
[4,1,1,1]
 => 3216
[3,3,1]
 => 3455
[3,2,2]
 => 3318
[3,2,1,1]
 => 5216
[3,1,1,1,1]
 => 2058
[2,2,2,1]
 => 1963
[2,2,1,1,1]
 => 1830
[2,1,1,1,1,1]
 => 725
[1,1,1,1,1,1,1]
 => 111
[8]
 => 951
[7,1]
 => 4883
[6,2]
 => 11756
[6,1,1]
 => 11530
[5,3]
 => 14623
[5,2,1]
 => 30987
Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on endofunctions.