Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001603
Mapping
St001603: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[3]
 => 1
[2,1]
 => 1
[1,1,1]
 => 1
[4]
 => 1
[3,1]
 => 1
[2,2]
 => 2
[2,1,1]
 => 2
[1,1,1,1]
 => 3
[5]
 => 1
[4,1]
 => 1
[3,2]
 => 2
[3,1,1]
 => 2
[2,2,1]
 => 4
[2,1,1,1]
 => 6
[1,1,1,1,1]
 => 12
[6]
 => 1
[5,1]
 => 1
[4,2]
 => 3
[4,1,1]
 => 3
[3,3]
 => 3
[3,2,1]
 => 6
[3,1,1,1]
 => 10
[2,2,2]
 => 11
[2,2,1,1]
 => 16
[2,1,1,1,1]
 => 30
[1,1,1,1,1,1]
 => 60
[7]
 => 1
[6,1]
 => 1
[5,2]
 => 3
[5,1,1]
 => 3
[4,3]
 => 4
[4,2,1]
 => 9
[4,1,1,1]
 => 15
[3,3,1]
 => 10
[3,2,2]
 => 18
[3,2,1,1]
 => 30
[3,1,1,1,1]
 => 60
[2,2,2,1]
 => 48
[2,2,1,1,1]
 => 90
[2,1,1,1,1,1]
 => 180
[1,1,1,1,1,1,1]
 => 360
[8]
 => 1
[7,1]
 => 1
[6,2]
 => 4
[6,1,1]
 => 4
[5,3]
 => 5
[5,2,1]
 => 12
[5,1,1,1]
 => 21
[4,4]
 => 8
[4,3,1]
 => 19
Description
The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. Two colourings are considered equal, if they are obtained by an action of the dihedral group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.