Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000089
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Mapping
Mp00102: Dyck paths —rise composition⟶ Integer compositions
St000089: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0]
 => [1] => 0
[1,0,1,0]
 => [1,1] => 0
[1,1,0,0]
 => [2] => 0
[1,0,1,0,1,0]
 => [1,1,1] => 0
[1,0,1,1,0,0]
 => [1,2] => 1
[1,1,0,0,1,0]
 => [2,1] => 1
[1,1,0,1,0,0]
 => [2,1] => 1
[1,1,1,0,0,0]
 => [3] => 0
[1,0,1,0,1,0,1,0]
 => [1,1,1,1] => 0
[1,0,1,0,1,1,0,0]
 => [1,1,2] => 1
[1,0,1,1,0,0,1,0]
 => [1,2,1] => 2
[1,0,1,1,0,1,0,0]
 => [1,2,1] => 2
[1,0,1,1,1,0,0,0]
 => [1,3] => 2
[1,1,0,0,1,0,1,0]
 => [2,1,1] => 1
[1,1,0,0,1,1,0,0]
 => [2,2] => 0
[1,1,0,1,0,0,1,0]
 => [2,1,1] => 1
[1,1,0,1,0,1,0,0]
 => [2,1,1] => 1
[1,1,0,1,1,0,0,0]
 => [2,2] => 0
[1,1,1,0,0,0,1,0]
 => [3,1] => 2
[1,1,1,0,0,1,0,0]
 => [3,1] => 2
[1,1,1,0,1,0,0,0]
 => [3,1] => 2
[1,1,1,1,0,0,0,0]
 => [4] => 0
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1] => 0
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,2] => 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,2,1] => 2
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,2,1] => 2
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,3] => 2
[1,0,1,1,0,0,1,0,1,0]
 => [1,2,1,1] => 2
[1,0,1,1,0,0,1,1,0,0]
 => [1,2,2] => 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,2,1,1] => 2
[1,0,1,1,0,1,0,1,0,0]
 => [1,2,1,1] => 2
[1,0,1,1,0,1,1,0,0,0]
 => [1,2,2] => 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,3,1] => 4
[1,0,1,1,1,0,0,1,0,0]
 => [1,3,1] => 4
[1,0,1,1,1,0,1,0,0,0]
 => [1,3,1] => 4
[1,0,1,1,1,1,0,0,0,0]
 => [1,4] => 3
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,1,1] => 1
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,2] => 2
[1,1,0,0,1,1,0,0,1,0]
 => [2,2,1] => 1
[1,1,0,0,1,1,0,1,0,0]
 => [2,2,1] => 1
[1,1,0,0,1,1,1,0,0,0]
 => [2,3] => 1
[1,1,0,1,0,0,1,0,1,0]
 => [2,1,1,1] => 1
[1,1,0,1,0,0,1,1,0,0]
 => [2,1,2] => 2
[1,1,0,1,0,1,0,0,1,0]
 => [2,1,1,1] => 1
[1,1,0,1,0,1,0,1,0,0]
 => [2,1,1,1] => 1
[1,1,0,1,0,1,1,0,0,0]
 => [2,1,2] => 2
[1,1,0,1,1,0,0,0,1,0]
 => [2,2,1] => 1
[1,1,0,1,1,0,0,1,0,0]
 => [2,2,1] => 1
[1,1,0,1,1,0,1,0,0,0]
 => [2,2,1] => 1
[1,1,0,1,1,1,0,0,0,0]
 => [2,3] => 1
Description
The absolute variation of a composition.