Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001200
Mapping
Mp00233: Dyck paths —skew partition⟶ Skew partitions
Mp00183: Skew partitions —inner shape⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St001200: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1,0,1,0,0,1,0]
 => [[3,3],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1],[2]]
 => [2]
 => [1,0,1,0]
 => 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]
 => 2
[1,1,0,0,1,1,0,0,1,0]
 => [[3,3,2],[2,1]]
 => [2,1]
 => [1,0,1,1,0,0]
 => 2
[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]
 => 2
[1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [[3,3,1,1],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,1],[1,1,1]]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 2
[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]
 => 2
[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]
 => 2
[1,0,1,1,1,0,0,1,0,0,1,0]
 => [[3,3,2,1],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,0,1,1,1,1,0,0,0,0,1,0]
 => [[3,3,3,1],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,1,0,0,1,0,1,0,1,0,1,0]
 => [[2,2,2,2,2],[1,1,1,1]]
 => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => 3
[1,1,0,0,1,0,1,0,1,1,0,0]
 => [[3,2,2,2],[1,1,1]]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 2
[1,1,0,0,1,0,1,1,0,0,1,0]
 => [[3,3,2,2],[2,1,1]]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 3
[1,1,0,0,1,0,1,1,1,0,0,0]
 => [[3,3,2,2],[1,1,1]]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 2
[1,1,0,0,1,1,0,0,1,0,1,0]
 => [[3,3,3,2],[2,2,1]]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => 2
[1,1,0,0,1,1,0,0,1,1,0,0]
 => [[4,3,2],[2,1]]
 => [2,1]
 => [1,0,1,1,0,0]
 => 2
[1,1,0,0,1,1,0,1,0,0,1,0]
 => [[4,4,2],[3,1]]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 3
[1,1,0,0,1,1,0,1,1,0,0,0]
 => [[4,4,2],[2,1]]
 => [2,1]
 => [1,0,1,1,0,0]
 => 2
[1,1,0,0,1,1,1,0,0,0,1,0]
 => [[3,3,3,2],[2,1,1]]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 3
[1,1,0,0,1,1,1,0,1,0,0,0]
 => [[3,3,3,2],[1,1,1]]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 2
[1,1,0,1,0,0,1,1,0,0,1,0]
 => [[4,4,3],[3,2]]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => 2
[1,1,0,1,0,0,1,1,0,1,0,0]
 => [[5,3],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,1,0,1,0,1,0,0,1,0,1,0]
 => [[4,4,4],[3,3]]
 => [3,3]
 => [1,1,1,0,1,0,0,0]
 => 2
[1,1,0,1,0,1,0,0,1,1,0,0]
 => [[5,4],[3]]
 => [3]
 => [1,0,1,0,1,0]
 => 3
[1,1,0,1,0,1,0,1,0,0,1,0]
 => [[5,5],[4]]
 => [4]
 => [1,0,1,0,1,0,1,0]
 => 3
[1,1,0,1,0,1,0,1,1,0,0,0]
 => [[5,5],[3]]
 => [3]
 => [1,0,1,0,1,0]
 => 3
[1,1,0,1,0,1,1,0,0,0,1,0]
 => [[4,4,4],[3,2]]
 => [3,2]
 => [1,0,1,1,1,0,0,0]
 => 2
[1,1,0,1,0,1,1,0,0,1,0,0]
 => [[5,4],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,1,0,1,0,1,1,1,0,0,0,0]
 => [[5,5],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,1,0,1,1,0,0,0,1,0,1,0]
 => [[3,3,3,3],[2,2,1]]
 => [2,2,1]
 => [1,1,1,0,0,1,0,0]
 => 2
[1,1,0,1,1,0,0,0,1,1,0,0]
 => [[4,3,3],[2,1]]
 => [2,1]
 => [1,0,1,1,0,0]
 => 2
[1,1,0,1,1,0,0,1,0,0,1,0]
 => [[4,4,3],[3,1]]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 3
[1,1,0,1,1,0,0,1,1,0,0,0]
 => [[4,4,3],[2,1]]
 => [2,1]
 => [1,0,1,1,0,0]
 => 2
[1,1,0,1,1,0,1,0,0,0,1,0]
 => [[3,3,3,3],[2,1,1]]
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 3
[1,1,0,1,1,0,1,0,1,0,0,0]
 => [[3,3,3,3],[1,1,1]]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 2
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [[4,4,4],[3,1]]
 => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 3
[1,1,0,1,1,1,0,0,1,0,0,0]
 => [[4,4,4],[2,1]]
 => [2,1]
 => [1,0,1,1,0,0]
 => 2
[1,1,1,0,0,0,1,0,1,0,1,0]
 => [[2,2,2,2,2],[1,1,1]]
 => [1,1,1]
 => [1,1,0,1,0,0]
 => 2
[1,1,1,0,0,0,1,1,0,0,1,0]
 => [[3,3,2,2],[2,1]]
 => [2,1]
 => [1,0,1,1,0,0]
 => 2
[1,1,1,0,0,1,0,0,1,1,0,0]
 => [[4,3,2],[2]]
 => [2]
 => [1,0,1,0]
 => 2
[1,1,1,0,0,1,0,1,0,0,1,0]
 => [[4,4,2],[3]]
 => [3]
 => [1,0,1,0,1,0]
 => 3
Description
The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.