Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001232
Mapping
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
Mp00296: Dyck paths —Knuth-Krattenthaler⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [.,.]
 => [1,0]
 => [1,0]
 => 0
[1,2] => [.,[.,.]]
 => [1,0,1,0]
 => [1,1,0,0]
 => 0
[2,1] => [[.,.],.]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1
[1,2,3] => [.,[.,[.,.]]]
 => [1,0,1,0,1,0]
 => [1,1,1,0,0,0]
 => 0
[1,3,2] => [.,[[.,.],.]]
 => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => 2
[3,1,2] => [[.,[.,.]],.]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 2
[3,2,1] => [[[.,.],.],.]
 => [1,1,1,0,0,0]
 => [1,1,0,0,1,0]
 => 1
[1,2,3,4] => [.,[.,[.,[.,.]]]]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1,0,0,0,0]
 => 0
[1,2,4,3] => [.,[.,[[.,.],.]]]
 => [1,0,1,0,1,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[1,4,2,3] => [.,[[.,[.,.]],.]]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => 4
[1,4,3,2] => [.,[[[.,.],.],.]]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
[2,1,3,4] => [[.,.],[.,[.,.]]]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[2,3,1,4] => [[.,.],[.,[.,.]]]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[2,3,4,1] => [[.,.],[.,[.,.]]]
 => [1,1,0,0,1,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[4,1,2,3] => [[.,[.,[.,.]]],.]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,1,1,0,0,0]
 => 3
[4,3,1,2] => [[[.,[.,.]],.],.]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[4,3,2,1] => [[[[.,.],.],.],.]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => 0
[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 6
[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 6
[1,5,4,2,3] => [.,[[[.,[.,.]],.],.]]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => 4
[1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 5
[3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 5
[3,1,4,5,2] => [[.,[.,.]],[.,[.,.]]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 5
[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5
[3,2,4,1,5] => [[[.,.],.],[.,[.,.]]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5
[3,2,4,5,1] => [[[.,.],.],[.,[.,.]]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5
[3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 5
[3,4,1,5,2] => [[.,[.,.]],[.,[.,.]]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 5
[3,4,2,1,5] => [[[.,.],.],[.,[.,.]]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5
[3,4,2,5,1] => [[[.,.],.],[.,[.,.]]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5
[3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 5
[3,4,5,2,1] => [[[.,.],.],[.,[.,.]]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5
[5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,1,1,1,0,0,0,0]
 => 4
[5,1,4,3,2] => [[.,[[[.,.],.],.]],.]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[5,2,1,3,4] => [[[.,.],[.,[.,.]]],.]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[5,2,3,1,4] => [[[.,.],[.,[.,.]]],.]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[5,2,3,4,1] => [[[.,.],[.,[.,.]]],.]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[5,4,1,2,3] => [[[.,[.,[.,.]]],.],.]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,0,1,1,1,0,0,0]
 => 3
[5,4,3,1,2] => [[[[.,[.,.]],.],.],.]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 2
[5,4,3,2,1] => [[[[[.,.],.],.],.],.]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
[1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 0
[1,2,3,4,6,5] => [.,[.,[.,[.,[[.,.],.]]]]]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.