Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001247
Mapping
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
St001247: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,0,0,1,0]
 => [2,1] => [[2,2],[1]]
 => [1]
 => 1
[1,0,1,1,0,0,1,0]
 => [1,2,1] => [[2,2,1],[1]]
 => [1]
 => 1
[1,1,0,0,1,0,1,0]
 => [2,1,1] => [[2,2,2],[1,1]]
 => [1,1]
 => 2
[1,1,0,0,1,1,0,0]
 => [2,2] => [[3,2],[1]]
 => [1]
 => 1
[1,1,0,1,0,0,1,0]
 => [3,1] => [[3,3],[2]]
 => [2]
 => 0
[1,1,1,0,0,0,1,0]
 => [3,1] => [[3,3],[2]]
 => [2]
 => 0
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,2,1] => [[2,2,1,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,2,1,1] => [[2,2,2,1],[1,1]]
 => [1,1]
 => 2
[1,0,1,1,0,0,1,1,0,0]
 => [1,2,2] => [[3,2,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,1] => [[3,3,1],[2]]
 => [2]
 => 0
[1,0,1,1,1,0,0,0,1,0]
 => [1,3,1] => [[3,3,1],[2]]
 => [2]
 => 0
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,1,1] => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => 3
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,2] => [[3,2,2],[1,1]]
 => [1,1]
 => 2
[1,1,0,0,1,1,0,0,1,0]
 => [2,2,1] => [[3,3,2],[2,1]]
 => [2,1]
 => 1
[1,1,0,0,1,1,0,1,0,0]
 => [2,3] => [[4,2],[1]]
 => [1]
 => 1
[1,1,0,0,1,1,1,0,0,0]
 => [2,3] => [[4,2],[1]]
 => [1]
 => 1
[1,1,0,1,0,0,1,0,1,0]
 => [3,1,1] => [[3,3,3],[2,2]]
 => [2,2]
 => 0
[1,1,0,1,0,0,1,1,0,0]
 => [3,2] => [[4,3],[2]]
 => [2]
 => 0
[1,1,0,1,0,1,0,0,1,0]
 => [4,1] => [[4,4],[3]]
 => [3]
 => 1
[1,1,0,1,1,0,0,0,1,0]
 => [4,1] => [[4,4],[3]]
 => [3]
 => 1
[1,1,1,0,0,0,1,0,1,0]
 => [3,1,1] => [[3,3,3],[2,2]]
 => [2,2]
 => 0
[1,1,1,0,0,0,1,1,0,0]
 => [3,2] => [[4,3],[2]]
 => [2]
 => 0
[1,1,1,0,0,1,0,0,1,0]
 => [4,1] => [[4,4],[3]]
 => [3]
 => 1
[1,1,1,0,1,0,0,0,1,0]
 => [4,1] => [[4,4],[3]]
 => [3]
 => 1
[1,1,1,1,0,0,0,0,1,0]
 => [4,1] => [[4,4],[3]]
 => [3]
 => 1
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,2,1] => [[2,2,1,1,1],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
 => [1,1]
 => 2
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,2,2] => [[3,2,1,1],[1]]
 => [1]
 => 1
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,3,1] => [[3,3,1,1],[2]]
 => [2]
 => 0
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,3,1] => [[3,3,1,1],[2]]
 => [2]
 => 0
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => 3
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,2,1,2] => [[3,2,2,1],[1,1]]
 => [1,1]
 => 2
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,2,2,1] => [[3,3,2,1],[2,1]]
 => [2,1]
 => 1
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,2,3] => [[4,2,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,2,3] => [[4,2,1],[1]]
 => [1]
 => 1
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,3,1,1] => [[3,3,3,1],[2,2]]
 => [2,2]
 => 0
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,3,2] => [[4,3,1],[2]]
 => [2]
 => 0
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,4,1] => [[4,4,1],[3]]
 => [3]
 => 1
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,4,1] => [[4,4,1],[3]]
 => [3]
 => 1
[1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,3,1,1] => [[3,3,3,1],[2,2]]
 => [2,2]
 => 0
[1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,3,2] => [[4,3,1],[2]]
 => [2]
 => 0
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,4,1] => [[4,4,1],[3]]
 => [3]
 => 1
[1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,4,1] => [[4,4,1],[3]]
 => [3]
 => 1
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,4,1] => [[4,4,1],[3]]
 => [3]
 => 1
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]]
 => [1,1,1,1]
 => 4
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [2,1,1,2] => [[3,2,2,2],[1,1,1]]
 => [1,1,1]
 => 3
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [2,1,2,1] => [[3,3,2,2],[2,1,1]]
 => [2,1,1]
 => 2
[1,1,0,0,1,0,1,1,0,1,0,0]
 => [2,1,3] => [[4,2,2],[1,1]]
 => [1,1]
 => 2
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [2,1,3] => [[4,2,2],[1,1]]
 => [1,1]
 => 2
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [2,2,1,1] => [[3,3,3,2],[2,2,1]]
 => [2,2,1]
 => 1
Description
The number of parts of a partition that are not congruent 2 modulo 3.