Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001232
Mapping
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [1] => [1] => [1,0]
 => 0
[[1,2]]
 => [1,2] => [1,2] => [1,0,1,0]
 => 1
[[1],[2]]
 => [2,1] => [2,1] => [1,1,0,0]
 => 0
[[1,3],[2]]
 => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => 1
[[1,2],[3]]
 => [3,1,2] => [1,3,2] => [1,0,1,1,0,0]
 => 2
[[1],[2],[3]]
 => [3,2,1] => [3,2,1] => [1,1,1,0,0,0]
 => 0
[[1,2,4],[3]]
 => [3,1,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 3
[[1,3],[2,4]]
 => [2,4,1,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
 => 2
[[1,4],[2],[3]]
 => [3,2,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
 => 1
[[1,3],[2],[4]]
 => [4,2,1,3] => [2,4,1,3] => [1,1,0,1,1,0,0,0]
 => 4
[[1,2],[3],[4]]
 => [4,3,1,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 3
[[1],[2],[3],[4]]
 => [4,3,2,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => 0
[[1,3,5],[2,4]]
 => [2,4,1,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
 => 3
[[1,2,4],[3,5]]
 => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
 => 4
[[1,3,5],[2],[4]]
 => [4,2,1,3,5] => [2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0]
 => 5
[[1,2,5],[3],[4]]
 => [4,3,1,2,5] => [1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
 => 4
[[1,3,4],[2],[5]]
 => [5,2,1,3,4] => [2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0]
 => 3
[[1,4],[2,5],[3]]
 => [3,2,5,1,4] => [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0]
 => 2
[[1,2],[3,5],[4]]
 => [4,3,5,1,2] => [1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => 5
[[1,3],[2,4],[5]]
 => [5,2,4,1,3] => [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
 => 3
[[1,5],[2],[3],[4]]
 => [4,3,2,1,5] => [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
 => 1
[[1,4],[2],[3],[5]]
 => [5,3,2,1,4] => [3,5,2,1,4] => [1,1,1,0,1,1,0,0,0,0]
 => 6
[[1,3],[2],[4],[5]]
 => [5,4,2,1,3] => [2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0]
 => 6
[[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => [1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
 => 4
[[1],[2],[3],[4],[5]]
 => [5,4,3,2,1] => [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => 0
[[1,2,4,6],[3,5]]
 => [3,5,1,2,4,6] => [1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0]
 => 5
[[1,3,4,6],[2],[5]]
 => [5,2,1,3,4,6] => [2,1,5,3,4,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 4
[[1,2,4,5],[3],[6]]
 => [6,3,1,2,4,5] => [1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0]
 => 5
[[1,3,5],[2,4,6]]
 => [2,4,6,1,3,5] => [2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0]
 => 4
[[1,4,6],[2,5],[3]]
 => [3,2,5,1,4,6] => [3,2,1,5,4,6] => [1,1,1,0,0,0,1,1,0,0,1,0]
 => 3
[[1,3,6],[2,4],[5]]
 => [5,2,4,1,3,6] => [2,1,5,4,3,6] => [1,1,0,0,1,1,1,0,0,0,1,0]
 => 4
[[1,3,5],[2,6],[4]]
 => [4,2,6,1,3,5] => [2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0]
 => 6
[[1,2,5],[3,6],[4]]
 => [4,3,6,1,2,5] => [1,4,3,2,6,5] => [1,0,1,1,1,0,0,0,1,1,0,0]
 => 5
[[1,3,4],[2,6],[5]]
 => [5,2,6,1,3,4] => [2,1,5,3,6,4] => [1,1,0,0,1,1,1,0,0,1,0,0]
 => 5
[[1,2,4],[3,5],[6]]
 => [6,3,5,1,2,4] => [1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0]
 => 5
[[1,4,6],[2],[3],[5]]
 => [5,3,2,1,4,6] => [3,5,2,1,4,6] => [1,1,1,0,1,1,0,0,0,0,1,0]
 => 7
[[1,3,6],[2],[4],[5]]
 => [5,4,2,1,3,6] => [2,5,4,1,3,6] => [1,1,0,1,1,1,0,0,0,0,1,0]
 => 7
[[1,2,6],[3],[4],[5]]
 => [5,4,3,1,2,6] => [1,5,4,3,2,6] => [1,0,1,1,1,1,0,0,0,0,1,0]
 => 5
[[1,4,5],[2],[3],[6]]
 => [6,3,2,1,4,5] => [3,2,6,1,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0]
 => 6
[[1,3,4],[2],[5],[6]]
 => [6,5,2,1,3,4] => [2,1,6,5,3,4] => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 4
[[1,4],[2,5],[3,6]]
 => [3,6,2,5,1,4] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0]
 => 3
[[1,2],[3,5],[4,6]]
 => [4,6,3,5,1,2] => [1,4,3,6,5,2] => [1,0,1,1,1,0,0,1,1,0,0,0]
 => 7
[[1,5],[2,6],[3],[4]]
 => [4,3,2,6,1,5] => [4,3,2,1,6,5] => [1,1,1,1,0,0,0,0,1,1,0,0]
 => 2
[[1,3],[2,6],[4],[5]]
 => [5,4,2,6,1,3] => [2,5,4,1,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0]
 => 8
[[1,2],[3,6],[4],[5]]
 => [5,4,3,6,1,2] => [1,5,4,3,6,2] => [1,0,1,1,1,1,0,0,0,1,0,0]
 => 6
[[1,4],[2,5],[3],[6]]
 => [6,3,2,5,1,4] => [3,2,6,1,5,4] => [1,1,1,0,0,1,1,1,0,0,0,0]
 => 6
[[1,3],[2,4],[5],[6]]
 => [6,5,2,4,1,3] => [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0]
 => 4
[[1,6],[2],[3],[4],[5]]
 => [5,4,3,2,1,6] => [5,4,3,2,1,6] => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1
[[1,5],[2],[3],[4],[6]]
 => [6,4,3,2,1,5] => [4,6,3,2,1,5] => [1,1,1,1,0,1,1,0,0,0,0,0]
 => 8
[[1,4],[2],[3],[5],[6]]
 => [6,5,3,2,1,4] => [3,6,5,2,1,4] => [1,1,1,0,1,1,1,0,0,0,0,0]
 => 9
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.