Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001531
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Mapping
St001531: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => 1
[1,1,0,0]
 => 2
[1,0,1,0,1,0]
 => 1
[1,0,1,1,0,0]
 => 2
[1,1,0,0,1,0]
 => 2
[1,1,0,1,0,0]
 => 4
[1,1,1,0,0,0]
 => 7
[1,0,1,0,1,0,1,0]
 => 1
[1,0,1,0,1,1,0,0]
 => 2
[1,0,1,1,0,0,1,0]
 => 2
[1,0,1,1,0,1,0,0]
 => 4
[1,0,1,1,1,0,0,0]
 => 7
[1,1,0,0,1,0,1,0]
 => 2
[1,1,0,0,1,1,0,0]
 => 4
[1,1,0,1,0,0,1,0]
 => 4
[1,1,0,1,0,1,0,0]
 => 8
[1,1,0,1,1,0,0,0]
 => 14
[1,1,1,0,0,0,1,0]
 => 7
[1,1,1,0,0,1,0,0]
 => 14
[1,1,1,0,1,0,0,0]
 => 25
[1,1,1,1,0,0,0,0]
 => 40
[1,0,1,0,1,0,1,0,1,0]
 => 1
[1,0,1,0,1,0,1,1,0,0]
 => 2
[1,0,1,0,1,1,0,0,1,0]
 => 2
[1,0,1,0,1,1,0,1,0,0]
 => 4
[1,0,1,0,1,1,1,0,0,0]
 => 7
[1,0,1,1,0,0,1,0,1,0]
 => 2
[1,0,1,1,0,0,1,1,0,0]
 => 4
[1,0,1,1,0,1,0,0,1,0]
 => 4
[1,0,1,1,0,1,0,1,0,0]
 => 8
[1,0,1,1,0,1,1,0,0,0]
 => 14
[1,0,1,1,1,0,0,0,1,0]
 => 7
[1,0,1,1,1,0,0,1,0,0]
 => 14
[1,0,1,1,1,0,1,0,0,0]
 => 25
[1,0,1,1,1,1,0,0,0,0]
 => 40
[1,1,0,0,1,0,1,0,1,0]
 => 2
[1,1,0,0,1,0,1,1,0,0]
 => 4
[1,1,0,0,1,1,0,0,1,0]
 => 4
[1,1,0,0,1,1,0,1,0,0]
 => 8
[1,1,0,0,1,1,1,0,0,0]
 => 14
[1,1,0,1,0,0,1,0,1,0]
 => 4
[1,1,0,1,0,0,1,1,0,0]
 => 8
[1,1,0,1,0,1,0,0,1,0]
 => 8
[1,1,0,1,0,1,0,1,0,0]
 => 16
[1,1,0,1,0,1,1,0,0,0]
 => 28
[1,1,0,1,1,0,0,0,1,0]
 => 14
[1,1,0,1,1,0,0,1,0,0]
 => 28
[1,1,0,1,1,0,1,0,0,0]
 => 50
[1,1,0,1,1,1,0,0,0,0]
 => 80
[1,1,1,0,0,0,1,0,1,0]
 => 7
Description
Number of partial orders contained in the poset determined by the Dyck path. A Dyck path determines a poset, where the relations correspond to boxes under the path (seen as a North-East path). This statistic is closely related to unicellular LLT polynomials and their e-expansion.