Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001492
Mapping
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001492: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,0,0,1,0]
 => [[2,2],[1]]
 => [1]
 => [1,0]
 => 2
[1,0,1,1,0,0,1,0]
 => [[2,2,1],[1]]
 => [1]
 => [1,0]
 => 2
[1,1,0,0,1,0,1,0]
 => [[2,2,2],[1,1]]
 => [1,1]
 => [1,1,0,0]
 => 3
[1,1,0,0,1,1,0,0]
 => [[3,2],[1]]
 => [1]
 => [1,0]
 => 2
[1,1,0,1,0,0,1,0]
 => [[3,3],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,1,0,1,1,0,0,0]
 => [[3,3],[1]]
 => [1]
 => [1,0]
 => 2
[1,1,1,0,0,0,1,0]
 => [[2,2,2],[1]]
 => [1]
 => [1,0]
 => 2
[1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1],[1]]
 => [1]
 => [1,0]
 => 2
[1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1],[1,1]]
 => [1,1]
 => [1,1,0,0]
 => 3
[1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1],[1]]
 => [1]
 => [1,0]
 => 2
[1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1],[1]]
 => [1]
 => [1,0]
 => 2
[1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1],[1]]
 => [1]
 => [1,0]
 => 2
[1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2],[1,1,1]]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 3
[1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2],[1,1]]
 => [1,1]
 => [1,1,0,0]
 => 3
[1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => [2,1]
 => [1,0,1,1,0,0]
 => 3
[1,1,0,0,1,1,0,1,0,0]
 => [[4,2],[1]]
 => [1]
 => [1,0]
 => 2
[1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2],[1,1]]
 => [1,1]
 => [1,1,0,0]
 => 3
[1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3],[2,2]]
 => [2,2]
 => [1,1,1,0,0,0]
 => 4
[1,1,0,1,0,0,1,1,0,0]
 => [[4,3],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,1,0,1,0,1,0,0,1,0]
 => [[4,4],[3]]
 => [3]
 => [1,0,1,0,1,0]
 => 3
[1,1,0,1,0,1,1,0,0,0]
 => [[4,4],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3],[2,1]]
 => [2,1]
 => [1,0,1,1,0,0]
 => 3
[1,1,0,1,1,0,0,1,0,0]
 => [[4,3],[1]]
 => [1]
 => [1,0]
 => 2
[1,1,0,1,1,0,1,0,0,0]
 => [[3,3,3],[1,1]]
 => [1,1]
 => [1,1,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => [[4,4],[1]]
 => [1]
 => [1,0]
 => 2
[1,1,1,0,0,0,1,0,1,0]
 => [[2,2,2,2],[1,1]]
 => [1,1]
 => [1,1,0,0]
 => 3
[1,1,1,0,0,0,1,1,0,0]
 => [[3,2,2],[1]]
 => [1]
 => [1,0]
 => 2
[1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,1,1,0,0,1,1,0,0,0]
 => [[3,3,2],[1]]
 => [1]
 => [1,0]
 => 2
[1,1,1,0,1,0,0,0,1,0]
 => [[2,2,2,2],[1]]
 => [1]
 => [1,0]
 => 2
[1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,1,1,1,0,0,1,0,0,0]
 => [[3,3,3],[1]]
 => [1]
 => [1,0]
 => 2
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [[2,2,1,1,1],[1]]
 => [1]
 => [1,0]
 => 2
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [[2,2,2,1,1],[1,1]]
 => [1,1]
 => [1,1,0,0]
 => 3
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [[3,2,1,1],[1]]
 => [1]
 => [1,0]
 => 2
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1,1],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [[3,3,1,1],[1]]
 => [1]
 => [1,0]
 => 2
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [[2,2,2,1,1],[1]]
 => [1]
 => [1,0]
 => 2
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 3
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [[3,2,2,1],[1,1]]
 => [1,1]
 => [1,1,0,0]
 => 3
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2,1],[2,1]]
 => [2,1]
 => [1,0,1,1,0,0]
 => 3
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [[4,2,1],[1]]
 => [1]
 => [1,0]
 => 2
[1,0,1,1,0,0,1,1,1,0,0,0]
 => [[3,3,2,1],[1,1]]
 => [1,1]
 => [1,1,0,0]
 => 3
[1,0,1,1,0,1,0,0,1,0,1,0]
 => [[3,3,3,1],[2,2]]
 => [2,2]
 => [1,1,1,0,0,0]
 => 4
[1,0,1,1,0,1,0,0,1,1,0,0]
 => [[4,3,1],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,0,1,1,0,1,0,1,0,0,1,0]
 => [[4,4,1],[3]]
 => [3]
 => [1,0,1,0,1,0]
 => 3
[1,0,1,1,0,1,0,1,1,0,0,0]
 => [[4,4,1],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,0,1,1,0,1,1,0,0,0,1,0]
 => [[3,3,3,1],[2,1]]
 => [2,1]
 => [1,0,1,1,0,0]
 => 3
[1,0,1,1,0,1,1,0,0,1,0,0]
 => [[4,3,1],[1]]
 => [1]
 => [1,0]
 => 2
Description
The number of simple modules that do not appear in the socle of the regular module or have no nontrivial selfextensions with the regular module in the corresponding Nakayama algebra.