Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001525
Mapping
Mp00201: Dyck paths —Ringel⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00027: Dyck paths —to partition⟶ Integer partitions
St001525: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,0,0]
 => [2,3,1] => [1,1,0,1,0,0]
 => [1]
 => 1
[1,0,1,1,0,0]
 => [3,1,4,2] => [1,1,1,0,0,1,0,0]
 => [2]
 => 0
[1,1,0,0,1,0]
 => [2,4,1,3] => [1,1,0,1,1,0,0,0]
 => [1,1]
 => 0
[1,1,1,0,0,0]
 => [2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [2,1]
 => 1
[1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0]
 => [3]
 => 0
[1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0]
 => [2,2]
 => 2
[1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0]
 => [3,2]
 => 1
[1,1,0,0,1,0,1,0]
 => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => 0
[1,1,0,0,1,1,0,0]
 => [2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0]
 => [3,1,1]
 => 1
[1,1,0,1,1,0,0,0]
 => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0]
 => [3]
 => 0
[1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0]
 => [2,2,1]
 => 1
[1,1,1,0,0,1,0,0]
 => [2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0]
 => [1,1,1]
 => 0
[1,1,1,1,0,0,0,0]
 => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
 => [3,2,1]
 => 2
[1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [4]
 => 0
[1,0,1,0,1,1,0,0,1,0]
 => [4,1,2,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [3,3]
 => 0
[1,0,1,0,1,1,1,0,0,0]
 => [4,1,2,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [4,3]
 => 0
[1,0,1,1,0,0,1,0,1,0]
 => [3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [2,2,2]
 => 0
[1,0,1,1,0,0,1,1,0,0]
 => [3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [4,2,2]
 => 0
[1,0,1,1,0,1,1,0,0,0]
 => [5,1,4,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [4]
 => 0
[1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,3,2]
 => 2
[1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [2,2,2]
 => 0
[1,0,1,1,1,1,0,0,0,0]
 => [3,1,4,5,6,2] => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [4,3,2]
 => 1
[1,1,0,0,1,0,1,0,1,0]
 => [2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1]
 => 0
[1,1,0,0,1,0,1,1,0,0]
 => [2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [4,1,1,1]
 => 1
[1,1,0,0,1,1,0,0,1,0]
 => [2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [3,3,1,1]
 => 0
[1,1,0,0,1,1,0,1,0,0]
 => [2,6,1,5,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1]
 => 0
[1,1,0,0,1,1,1,0,0,0]
 => [2,4,1,5,6,3] => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [4,3,1,1]
 => 1
[1,1,0,1,0,0,1,1,0,0]
 => [5,3,1,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [4]
 => 0
[1,1,0,1,0,1,0,1,0,0]
 => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0]
 => [1]
 => 1
[1,1,0,1,0,1,1,0,0,0]
 => [5,4,1,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [4]
 => 0
[1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [3,3]
 => 0
[1,1,0,1,1,1,0,0,0,0]
 => [4,3,1,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [4,3]
 => 0
[1,1,1,0,0,0,1,0,1,0]
 => [2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,2,2,1]
 => 0
[1,1,1,0,0,0,1,1,0,0]
 => [2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [4,2,2,1]
 => 1
[1,1,1,0,0,1,0,0,1,0]
 => [2,6,4,1,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1]
 => 0
[1,1,1,0,0,1,0,1,0,0]
 => [2,6,5,1,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1]
 => 0
[1,1,1,0,0,1,1,0,0,0]
 => [2,5,4,1,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [4,1,1,1]
 => 1
[1,1,1,0,1,1,0,0,0,0]
 => [5,3,4,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [4]
 => 0
[1,1,1,1,0,0,0,0,1,0]
 => [2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [3,3,2,1]
 => 1
[1,1,1,1,0,0,0,1,0,0]
 => [2,3,6,5,1,4] => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,2,2,1]
 => 0
[1,1,1,1,0,0,1,0,0,0]
 => [2,6,4,5,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1]
 => 0
[1,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [4,3,2,1]
 => 2
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [6,1,2,3,4,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => [5]
 => 0
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [5,1,2,3,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0]
 => [4,4]
 => 0
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [5,1,2,3,6,7,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0]
 => [5,4]
 => 0
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [4,1,2,7,3,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => [3,3,3]
 => 3
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [4,1,2,6,3,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0]
 => [5,3,3]
 => 2
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [6,1,2,5,3,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
 => [5]
 => 0
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [4,1,2,5,7,3,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0]
 => [4,4,3]
 => 1
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [4,1,2,7,6,3,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0]
 => [3,3,3]
 => 3
Description
The number of symmetric hooks on the diagonal of a partition.