Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000905
(load all 91 compositions to match this statistic)
Mapping
St000905: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 1
[1,1] => 1
[2] => 1
[1,1,1] => 1
[1,2] => 1
[2,1] => 1
[3] => 1
[1,1,1,1] => 1
[1,1,2] => 2
[1,2,1] => 2
[1,3] => 1
[2,1,1] => 2
[2,2] => 1
[3,1] => 1
[4] => 1
[1,1,1,1,1] => 1
[1,1,1,2] => 2
[1,1,2,1] => 2
[1,1,3] => 2
[1,2,1,1] => 2
[1,2,2] => 2
[1,3,1] => 2
[1,4] => 1
[2,1,1,1] => 2
[2,1,2] => 2
[2,2,1] => 2
[2,3] => 1
[3,1,1] => 2
[3,2] => 1
[4,1] => 1
[5] => 1
[1,1,1,1,1,1] => 1
[1,1,1,1,2] => 2
[1,1,1,2,1] => 2
[1,1,1,3] => 2
[1,1,2,1,1] => 2
[1,1,2,2] => 1
[1,1,3,1] => 2
[1,1,4] => 2
[1,2,1,1,1] => 2
[1,2,1,2] => 1
[1,2,2,1] => 1
[1,2,3] => 1
[1,3,1,1] => 2
[1,3,2] => 1
[1,4,1] => 2
[1,5] => 1
[2,1,1,1,1] => 2
[2,1,1,2] => 1
[2,1,2,1] => 1
Description
The number of different multiplicities of parts of an integer composition.
Matching statistic: St000897
Mapping
Mp00040: Integer compositions —to partition⟶ Integer partitions
St000897: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1]
 => 1
[1,1] => [1,1]
 => 1
[2] => [2]
 => 1
[1,1,1] => [1,1,1]
 => 1
[1,2] => [2,1]
 => 1
[2,1] => [2,1]
 => 1
[3] => [3]
 => 1
[1,1,1,1] => [1,1,1,1]
 => 1
[1,1,2] => [2,1,1]
 => 2
[1,2,1] => [2,1,1]
 => 2
[1,3] => [3,1]
 => 1
[2,1,1] => [2,1,1]
 => 2
[2,2] => [2,2]
 => 1
[3,1] => [3,1]
 => 1
[4] => [4]
 => 1
[1,1,1,1,1] => [1,1,1,1,1]
 => 1
[1,1,1,2] => [2,1,1,1]
 => 2
[1,1,2,1] => [2,1,1,1]
 => 2
[1,1,3] => [3,1,1]
 => 2
[1,2,1,1] => [2,1,1,1]
 => 2
[1,2,2] => [2,2,1]
 => 2
[1,3,1] => [3,1,1]
 => 2
[1,4] => [4,1]
 => 1
[2,1,1,1] => [2,1,1,1]
 => 2
[2,1,2] => [2,2,1]
 => 2
[2,2,1] => [2,2,1]
 => 2
[2,3] => [3,2]
 => 1
[3,1,1] => [3,1,1]
 => 2
[3,2] => [3,2]
 => 1
[4,1] => [4,1]
 => 1
[5] => [5]
 => 1
[1,1,1,1,1,1] => [1,1,1,1,1,1]
 => 1
[1,1,1,1,2] => [2,1,1,1,1]
 => 2
[1,1,1,2,1] => [2,1,1,1,1]
 => 2
[1,1,1,3] => [3,1,1,1]
 => 2
[1,1,2,1,1] => [2,1,1,1,1]
 => 2
[1,1,2,2] => [2,2,1,1]
 => 1
[1,1,3,1] => [3,1,1,1]
 => 2
[1,1,4] => [4,1,1]
 => 2
[1,2,1,1,1] => [2,1,1,1,1]
 => 2
[1,2,1,2] => [2,2,1,1]
 => 1
[1,2,2,1] => [2,2,1,1]
 => 1
[1,2,3] => [3,2,1]
 => 1
[1,3,1,1] => [3,1,1,1]
 => 2
[1,3,2] => [3,2,1]
 => 1
[1,4,1] => [4,1,1]
 => 2
[1,5] => [5,1]
 => 1
[2,1,1,1,1] => [2,1,1,1,1]
 => 2
[2,1,1,2] => [2,2,1,1]
 => 1
[2,1,2,1] => [2,2,1,1]
 => 1
Description
The number of different multiplicities of parts of an integer partition.