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Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001237
Mp00180: Integer compositions —to ribbon⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001237: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
St001237: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[2,1] => [[2,2],[1]]
=> [1]
=> [1,0,1,0]
=> 3
[1,2,1] => [[2,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 3
[2,1,1] => [[2,2,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 4
[2,2] => [[3,2],[1]]
=> [1]
=> [1,0,1,0]
=> 3
[3,1] => [[3,3],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 3
[1,1,2,1] => [[2,2,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 3
[1,2,1,1] => [[2,2,2,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 4
[1,2,2] => [[3,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 3
[1,3,1] => [[3,3,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 3
[2,1,1,1] => [[2,2,2,2],[1,1,1]]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 5
[2,1,2] => [[3,2,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 4
[2,2,1] => [[3,3,2],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 4
[2,3] => [[4,2],[1]]
=> [1]
=> [1,0,1,0]
=> 3
[3,1,1] => [[3,3,3],[2,2]]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 4
[3,2] => [[4,3],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 3
[4,1] => [[4,4],[3]]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 4
[1,1,1,2,1] => [[2,2,1,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 3
[1,1,2,1,1] => [[2,2,2,1,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 4
[1,1,2,2] => [[3,2,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 3
[1,1,3,1] => [[3,3,1,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 3
[1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 5
[1,2,1,2] => [[3,2,2,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 4
[1,2,2,1] => [[3,3,2,1],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 4
[1,2,3] => [[4,2,1],[1]]
=> [1]
=> [1,0,1,0]
=> 3
[1,3,1,1] => [[3,3,3,1],[2,2]]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 4
[1,3,2] => [[4,3,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 3
[1,4,1] => [[4,4,1],[3]]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 4
[2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]]
=> [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> 6
[2,1,1,2] => [[3,2,2,2],[1,1,1]]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 5
[2,1,2,1] => [[3,3,2,2],[2,1,1]]
=> [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> 5
[2,1,3] => [[4,2,2],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 4
[2,2,1,1] => [[3,3,3,2],[2,2,1]]
=> [2,2,1]
=> [1,0,1,0,1,1,0,0]
=> 5
[2,2,2] => [[4,3,2],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 4
[2,3,1] => [[4,4,2],[3,1]]
=> [3,1]
=> [1,1,0,1,0,0,1,0]
=> 4
[2,4] => [[5,2],[1]]
=> [1]
=> [1,0,1,0]
=> 3
[3,1,1,1] => [[3,3,3,3],[2,2,2]]
=> [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> 5
[3,1,2] => [[4,3,3],[2,2]]
=> [2,2]
=> [1,1,0,0,1,1,0,0]
=> 4
[3,2,1] => [[4,4,3],[3,2]]
=> [3,2]
=> [1,1,0,0,1,0,1,0]
=> 4
[3,3] => [[5,3],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 3
[4,1,1] => [[4,4,4],[3,3]]
=> [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> 5
[4,2] => [[5,4],[3]]
=> [3]
=> [1,1,1,0,0,0,1,0]
=> 4
[5,1] => [[5,5],[4]]
=> [4]
=> [1,1,1,1,0,0,0,0,1,0]
=> 5
[1,1,1,1,2,1] => [[2,2,1,1,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 3
[1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 4
[1,1,1,2,2] => [[3,2,1,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 3
[1,1,1,3,1] => [[3,3,1,1,1],[2]]
=> [2]
=> [1,1,0,0,1,0]
=> 3
[1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]]
=> [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> 5
[1,1,2,1,2] => [[3,2,2,1,1],[1,1]]
=> [1,1]
=> [1,0,1,1,0,0]
=> 4
[1,1,2,2,1] => [[3,3,2,1,1],[2,1]]
=> [2,1]
=> [1,0,1,0,1,0]
=> 4
[1,1,2,3] => [[4,2,1,1],[1]]
=> [1]
=> [1,0,1,0]
=> 3
Description
The number of simple modules with injective dimension at most one or dominant dimension at least one.
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