Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001232
(load all 4 compositions to match this statistic)
Mapping
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
Mp00132: Dyck paths —switch returns and last double rise⟶ 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]
 => [1,0,1,0]
 => 1
[2,1] => [[.,.],.]
 => [1,1,0,0]
 => [1,1,0,0]
 => 0
[1,3,2] => [.,[[.,.],.]]
 => [1,0,1,1,0,0]
 => [1,1,0,1,0,0]
 => 2
[2,1,3] => [[.,.],[.,.]]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 1
[2,3,1] => [[.,[.,.]],.]
 => [1,1,0,1,0,0]
 => [1,0,1,1,0,0]
 => 2
[3,1,2] => [[.,.],[.,.]]
 => [1,1,0,0,1,0]
 => [1,1,0,0,1,0]
 => 1
[3,2,1] => [[[.,.],.],.]
 => [1,1,1,0,0,0]
 => [1,1,1,0,0,0]
 => 0
[1,4,3,2] => [.,[[[.,.],.],.]]
 => [1,0,1,1,1,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3
[2,1,4,3] => [[.,.],[[.,.],.]]
 => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
[2,3,1,4] => [[.,[.,.]],[.,.]]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[2,4,1,3] => [[.,[.,.]],[.,.]]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[2,4,3,1] => [[.,[[.,.],.]],.]
 => [1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,0]
 => 4
[3,1,4,2] => [[.,.],[[.,.],.]]
 => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
[3,2,1,4] => [[[.,.],.],[.,.]]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[3,2,4,1] => [[[.,.],[.,.]],.]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[3,4,1,2] => [[.,[.,.]],[.,.]]
 => [1,1,0,1,0,0,1,0]
 => [1,0,1,1,0,0,1,0]
 => 3
[3,4,2,1] => [[[.,[.,.]],.],.]
 => [1,1,1,0,1,0,0,0]
 => [1,0,1,1,1,0,0,0]
 => 3
[4,1,3,2] => [[.,.],[[.,.],.]]
 => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,0,0]
 => 2
[4,2,1,3] => [[[.,.],.],[.,.]]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[4,2,3,1] => [[[.,.],[.,.]],.]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,0,1,1,0,0]
 => 2
[4,3,1,2] => [[[.,.],.],[.,.]]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,0,1,0]
 => 1
[4,3,2,1] => [[[[.,.],.],.],.]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => 0
[1,4,3,5,2] => [.,[[[.,.],[.,.]],.]]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 5
[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,0,1,1,1,0,0,1,0,0]
 => 5
[1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[2,4,3,1,5] => [[.,[[.,.],.]],[.,.]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5
[2,5,3,1,4] => [[.,[[.,.],.]],[.,.]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5
[2,5,4,1,3] => [[.,[[.,.],.]],[.,.]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5
[2,5,4,3,1] => [[.,[[[.,.],.],.]],.]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => 6
[3,1,5,4,2] => [[.,.],[[[.,.],.],.]]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[3,2,4,1,5] => [[[.,.],[.,.]],[.,.]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[3,2,5,1,4] => [[[.,.],[.,.]],[.,.]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[3,2,5,4,1] => [[[.,.],[[.,.],.]],.]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => 4
[3,4,2,1,5] => [[[.,[.,.]],.],[.,.]]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[3,4,2,5,1] => [[[.,[.,.]],[.,.]],.]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[3,5,2,1,4] => [[[.,[.,.]],.],[.,.]]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,0,1,1,1,0,0,0,1,0]
 => 4
[3,5,2,4,1] => [[[.,[.,.]],[.,.]],.]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,0,1,1,0,0,1,1,0,0]
 => 4
[3,5,4,1,2] => [[.,[[.,.],.]],[.,.]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,0,0,1,0]
 => 5
[3,5,4,2,1] => [[[.,[[.,.],.]],.],.]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => 6
[4,1,5,3,2] => [[.,.],[[[.,.],.],.]]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => 3
[4,2,1,5,3] => [[[.,.],.],[[.,.],.]]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[4,2,3,1,5] => [[[.,.],[.,.]],[.,.]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[4,2,5,1,3] => [[[.,.],[.,.]],[.,.]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,0,1,1,0,0,1,0]
 => 3
[4,2,5,3,1] => [[[.,.],[[.,.],.]],.]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => 4
[4,3,1,5,2] => [[[.,.],.],[[.,.],.]]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => 2
[4,3,2,1,5] => [[[[.,.],.],.],[.,.]]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
[4,3,2,5,1] => [[[[.,.],.],[.,.]],.]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,0,0,1,1,0,0]
 => 2
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.