Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001031
Mapping
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
St001031: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => [1,1] => [2] => [1,1,0,0]
 => 1
[1,0,1,0,1,0]
 => [1,1,1] => [3] => [1,1,1,0,0,0]
 => 1
[1,0,1,1,0,0]
 => [1,2] => [1,1] => [1,0,1,0]
 => 0
[1,1,0,0,1,0]
 => [2,1] => [1,1] => [1,0,1,0]
 => 0
[1,0,1,0,1,0,1,0]
 => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0]
 => 2
[1,0,1,0,1,1,0,0]
 => [1,1,2] => [2,1] => [1,1,0,0,1,0]
 => 1
[1,0,1,1,0,0,1,0]
 => [1,2,1] => [1,1,1] => [1,0,1,0,1,0]
 => 0
[1,0,1,1,0,1,0,0]
 => [1,3] => [1,1] => [1,0,1,0]
 => 0
[1,0,1,1,1,0,0,0]
 => [1,3] => [1,1] => [1,0,1,0]
 => 0
[1,1,0,0,1,0,1,0]
 => [2,1,1] => [1,2] => [1,0,1,1,0,0]
 => 1
[1,1,0,0,1,1,0,0]
 => [2,2] => [2] => [1,1,0,0]
 => 1
[1,1,0,1,0,0,1,0]
 => [3,1] => [1,1] => [1,0,1,0]
 => 0
[1,1,1,0,0,0,1,0]
 => [3,1] => [1,1] => [1,0,1,0]
 => 0
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0]
 => 2
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0]
 => 1
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => 1
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,3] => [2,1] => [1,1,0,0,1,0]
 => 1
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,3] => [2,1] => [1,1,0,0,1,0]
 => 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0]
 => 1
[1,0,1,1,0,0,1,1,0,0]
 => [1,2,2] => [1,2] => [1,0,1,1,0,0]
 => 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,1] => [1,1,1] => [1,0,1,0,1,0]
 => 0
[1,0,1,1,0,1,0,1,0,0]
 => [1,4] => [1,1] => [1,0,1,0]
 => 0
[1,0,1,1,0,1,1,0,0,0]
 => [1,4] => [1,1] => [1,0,1,0]
 => 0
[1,0,1,1,1,0,0,0,1,0]
 => [1,3,1] => [1,1,1] => [1,0,1,0,1,0]
 => 0
[1,0,1,1,1,0,0,1,0,0]
 => [1,4] => [1,1] => [1,0,1,0]
 => 0
[1,0,1,1,1,0,1,0,0,0]
 => [1,4] => [1,1] => [1,0,1,0]
 => 0
[1,0,1,1,1,1,0,0,0,0]
 => [1,4] => [1,1] => [1,0,1,0]
 => 0
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0]
 => 1
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,2] => [1,1,1] => [1,0,1,0,1,0]
 => 0
[1,1,0,0,1,1,0,0,1,0]
 => [2,2,1] => [2,1] => [1,1,0,0,1,0]
 => 1
[1,1,0,0,1,1,0,1,0,0]
 => [2,3] => [1,1] => [1,0,1,0]
 => 0
[1,1,0,0,1,1,1,0,0,0]
 => [2,3] => [1,1] => [1,0,1,0]
 => 0
[1,1,0,1,0,0,1,0,1,0]
 => [3,1,1] => [1,2] => [1,0,1,1,0,0]
 => 1
[1,1,0,1,0,0,1,1,0,0]
 => [3,2] => [1,1] => [1,0,1,0]
 => 0
[1,1,0,1,0,1,0,0,1,0]
 => [4,1] => [1,1] => [1,0,1,0]
 => 0
[1,1,0,1,1,0,0,0,1,0]
 => [4,1] => [1,1] => [1,0,1,0]
 => 0
[1,1,1,0,0,0,1,0,1,0]
 => [3,1,1] => [1,2] => [1,0,1,1,0,0]
 => 1
[1,1,1,0,0,0,1,1,0,0]
 => [3,2] => [1,1] => [1,0,1,0]
 => 0
[1,1,1,0,0,1,0,0,1,0]
 => [4,1] => [1,1] => [1,0,1,0]
 => 0
[1,1,1,0,1,0,0,0,1,0]
 => [4,1] => [1,1] => [1,0,1,0]
 => 0
[1,1,1,1,0,0,0,0,1,0]
 => [4,1] => [1,1] => [1,0,1,0]
 => 0
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 3
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0]
 => 2
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
 => 1
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0]
 => 1
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0]
 => 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
 => 1
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0]
 => 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0]
 => 1
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,4] => [2,1] => [1,1,0,0,1,0]
 => 1
Description
The height of the bicoloured Motzkin path associated with the Dyck path.