Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000016
(load all 55 compositions to match this statistic)
Mapping
St000016: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => 0
[[1,2]]
 => 1
[[1],[2]]
 => 0
[[1,2,3]]
 => 3
[[1,3],[2]]
 => 1
[[1,2],[3]]
 => 1
[[1],[2],[3]]
 => 0
[[1,2,3,4]]
 => 6
[[1,3,4],[2]]
 => 3
[[1,2,4],[3]]
 => 3
[[1,2,3],[4]]
 => 3
[[1,3],[2,4]]
 => 3
[[1,2],[3,4]]
 => 3
[[1,4],[2],[3]]
 => 1
[[1,3],[2],[4]]
 => 1
[[1,2],[3],[4]]
 => 1
[[1],[2],[3],[4]]
 => 0
[[1,2,3,4,5]]
 => 10
[[1,3,4,5],[2]]
 => 6
[[1,2,4,5],[3]]
 => 6
[[1,2,3,5],[4]]
 => 6
[[1,2,3,4],[5]]
 => 6
[[1,3,5],[2,4]]
 => 5
[[1,2,5],[3,4]]
 => 5
[[1,3,4],[2,5]]
 => 5
[[1,2,4],[3,5]]
 => 5
[[1,2,3],[4,5]]
 => 5
[[1,4,5],[2],[3]]
 => 3
[[1,3,5],[2],[4]]
 => 3
[[1,2,5],[3],[4]]
 => 3
[[1,3,4],[2],[5]]
 => 3
[[1,2,4],[3],[5]]
 => 3
[[1,2,3],[4],[5]]
 => 3
[[1,4],[2,5],[3]]
 => 3
[[1,3],[2,5],[4]]
 => 3
[[1,2],[3,5],[4]]
 => 3
[[1,3],[2,4],[5]]
 => 3
[[1,2],[3,4],[5]]
 => 3
[[1,5],[2],[3],[4]]
 => 1
[[1,4],[2],[3],[5]]
 => 1
[[1,3],[2],[4],[5]]
 => 1
[[1,2],[3],[4],[5]]
 => 1
[[1],[2],[3],[4],[5]]
 => 0
[[1,2,3,4,5,6]]
 => 15
[[1,3,4,5,6],[2]]
 => 10
[[1,2,4,5,6],[3]]
 => 10
[[1,2,3,5,6],[4]]
 => 10
[[1,2,3,4,6],[5]]
 => 10
[[1,2,3,4,5],[6]]
 => 10
[[1,3,5,6],[2,4]]
 => 8
Description
The number of attacking pairs of a standard tableau. Note that this is actually a statistic on the underlying partition. A pair of cells $(c, d)$ of a Young diagram (in English notation) is said to be attacking if one of the following conditions holds: 1. $c$ and $d$ lie in the same row with $c$ strictly to the west of $d$. 2. $c$ is in the row immediately to the south of $d$, and $c$ lies strictly east of $d$.
Matching statistic: St001232
Mapping
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00012: Binary trees —to Dyck path: up step, left tree, down step, right tree⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 12%
Values
[[1]]
 => [1] => [.,.]
 => [1,0]
 => 0
[[1,2]]
 => [1,2] => [.,[.,.]]
 => [1,0,1,0]
 => 1
[[1],[2]]
 => [2,1] => [[.,.],.]
 => [1,1,0,0]
 => 0
[[1,2,3]]
 => [1,2,3] => [.,[.,[.,.]]]
 => [1,0,1,0,1,0]
 => ? = 3
[[1,3],[2]]
 => [2,1,3] => [[.,.],[.,.]]
 => [1,1,0,0,1,0]
 => 1
[[1,2],[3]]
 => [3,1,2] => [[.,.],[.,.]]
 => [1,1,0,0,1,0]
 => 1
[[1],[2],[3]]
 => [3,2,1] => [[[.,.],.],.]
 => [1,1,1,0,0,0]
 => 0
[[1,2,3,4]]
 => [1,2,3,4] => [.,[.,[.,[.,.]]]]
 => [1,0,1,0,1,0,1,0]
 => ? = 6
[[1,3,4],[2]]
 => [2,1,3,4] => [[.,.],[.,[.,.]]]
 => [1,1,0,0,1,0,1,0]
 => ? = 3
[[1,2,4],[3]]
 => [3,1,2,4] => [[.,.],[.,[.,.]]]
 => [1,1,0,0,1,0,1,0]
 => ? = 3
[[1,2,3],[4]]
 => [4,1,2,3] => [[.,.],[.,[.,.]]]
 => [1,1,0,0,1,0,1,0]
 => ? = 3
[[1,3],[2,4]]
 => [2,4,1,3] => [[.,[.,.]],[.,.]]
 => [1,1,0,1,0,0,1,0]
 => ? = 3
[[1,2],[3,4]]
 => [3,4,1,2] => [[.,[.,.]],[.,.]]
 => [1,1,0,1,0,0,1,0]
 => ? = 3
[[1,4],[2],[3]]
 => [3,2,1,4] => [[[.,.],.],[.,.]]
 => [1,1,1,0,0,0,1,0]
 => 1
[[1,3],[2],[4]]
 => [4,2,1,3] => [[[.,.],.],[.,.]]
 => [1,1,1,0,0,0,1,0]
 => 1
[[1,2],[3],[4]]
 => [4,3,1,2] => [[[.,.],.],[.,.]]
 => [1,1,1,0,0,0,1,0]
 => 1
[[1],[2],[3],[4]]
 => [4,3,2,1] => [[[[.,.],.],.],.]
 => [1,1,1,1,0,0,0,0]
 => 0
[[1,2,3,4,5]]
 => [1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 10
[[1,3,4,5],[2]]
 => [2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 6
[[1,2,4,5],[3]]
 => [3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 6
[[1,2,3,5],[4]]
 => [4,1,2,3,5] => [[.,.],[.,[.,[.,.]]]]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 6
[[1,2,3,4],[5]]
 => [5,1,2,3,4] => [[.,.],[.,[.,[.,.]]]]
 => [1,1,0,0,1,0,1,0,1,0]
 => ? = 6
[[1,3,5],[2,4]]
 => [2,4,1,3,5] => [[.,[.,.]],[.,[.,.]]]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 5
[[1,2,5],[3,4]]
 => [3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 5
[[1,3,4],[2,5]]
 => [2,5,1,3,4] => [[.,[.,.]],[.,[.,.]]]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 5
[[1,2,4],[3,5]]
 => [3,5,1,2,4] => [[.,[.,.]],[.,[.,.]]]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 5
[[1,2,3],[4,5]]
 => [4,5,1,2,3] => [[.,[.,.]],[.,[.,.]]]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 5
[[1,4,5],[2],[3]]
 => [3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 3
[[1,3,5],[2],[4]]
 => [4,2,1,3,5] => [[[.,.],.],[.,[.,.]]]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 3
[[1,2,5],[3],[4]]
 => [4,3,1,2,5] => [[[.,.],.],[.,[.,.]]]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 3
[[1,3,4],[2],[5]]
 => [5,2,1,3,4] => [[[.,.],.],[.,[.,.]]]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 3
[[1,2,4],[3],[5]]
 => [5,3,1,2,4] => [[[.,.],.],[.,[.,.]]]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 3
[[1,2,3],[4],[5]]
 => [5,4,1,2,3] => [[[.,.],.],[.,[.,.]]]
 => [1,1,1,0,0,0,1,0,1,0]
 => ? = 3
[[1,4],[2,5],[3]]
 => [3,2,5,1,4] => [[[.,.],[.,.]],[.,.]]
 => [1,1,1,0,0,1,0,0,1,0]
 => ? = 3
[[1,3],[2,5],[4]]
 => [4,2,5,1,3] => [[[.,.],[.,.]],[.,.]]
 => [1,1,1,0,0,1,0,0,1,0]
 => ? = 3
[[1,2],[3,5],[4]]
 => [4,3,5,1,2] => [[[.,.],[.,.]],[.,.]]
 => [1,1,1,0,0,1,0,0,1,0]
 => ? = 3
[[1,3],[2,4],[5]]
 => [5,2,4,1,3] => [[[.,.],[.,.]],[.,.]]
 => [1,1,1,0,0,1,0,0,1,0]
 => ? = 3
[[1,2],[3,4],[5]]
 => [5,3,4,1,2] => [[[.,.],[.,.]],[.,.]]
 => [1,1,1,0,0,1,0,0,1,0]
 => ? = 3
[[1,5],[2],[3],[4]]
 => [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] => [[[[.,.],.],.],[.,.]]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
[[1,3],[2],[4],[5]]
 => [5,4,2,1,3] => [[[[.,.],.],.],[.,.]]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
[[1,2],[3],[4],[5]]
 => [5,4,3,1,2] => [[[[.,.],.],.],[.,.]]
 => [1,1,1,1,0,0,0,0,1,0]
 => 1
[[1],[2],[3],[4],[5]]
 => [5,4,3,2,1] => [[[[[.,.],.],.],.],.]
 => [1,1,1,1,1,0,0,0,0,0]
 => 0
[[1,2,3,4,5,6]]
 => [1,2,3,4,5,6] => [.,[.,[.,[.,[.,[.,.]]]]]]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 15
[[1,3,4,5,6],[2]]
 => [2,1,3,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 10
[[1,2,4,5,6],[3]]
 => [3,1,2,4,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 10
[[1,2,3,5,6],[4]]
 => [4,1,2,3,5,6] => [[.,.],[.,[.,[.,[.,.]]]]]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 10
[[1,2,3,4,6],[5]]
 => [5,1,2,3,4,6] => [[.,.],[.,[.,[.,[.,.]]]]]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 10
[[1,2,3,4,5],[6]]
 => [6,1,2,3,4,5] => [[.,.],[.,[.,[.,[.,.]]]]]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => ? = 10
[[1,3,5,6],[2,4]]
 => [2,4,1,3,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 8
[[1,2,5,6],[3,4]]
 => [3,4,1,2,5,6] => [[.,[.,.]],[.,[.,[.,.]]]]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 8
[[1,3,4,6],[2,5]]
 => [2,5,1,3,4,6] => [[.,[.,.]],[.,[.,[.,.]]]]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 8
[[1,2,4,6],[3,5]]
 => [3,5,1,2,4,6] => [[.,[.,.]],[.,[.,[.,.]]]]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 8
[[1,2,3,6],[4,5]]
 => [4,5,1,2,3,6] => [[.,[.,.]],[.,[.,[.,.]]]]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 8
[[1,3,4,5],[2,6]]
 => [2,6,1,3,4,5] => [[.,[.,.]],[.,[.,[.,.]]]]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 8
[[1,2,4,5],[3,6]]
 => [3,6,1,2,4,5] => [[.,[.,.]],[.,[.,[.,.]]]]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 8
[[1,2,3,5],[4,6]]
 => [4,6,1,2,3,5] => [[.,[.,.]],[.,[.,[.,.]]]]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 8
[[1,2,3,4],[5,6]]
 => [5,6,1,2,3,4] => [[.,[.,.]],[.,[.,[.,.]]]]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 8
[[1,4,5,6],[2],[3]]
 => [3,2,1,4,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 6
[[1,3,5,6],[2],[4]]
 => [4,2,1,3,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 6
[[1,2,5,6],[3],[4]]
 => [4,3,1,2,5,6] => [[[.,.],.],[.,[.,[.,.]]]]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 6
[[1,3,4,6],[2],[5]]
 => [5,2,1,3,4,6] => [[[.,.],.],[.,[.,[.,.]]]]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 6
[[1,2,4,6],[3],[5]]
 => [5,3,1,2,4,6] => [[[.,.],.],[.,[.,[.,.]]]]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 6
[[1,2,3,6],[4],[5]]
 => [5,4,1,2,3,6] => [[[.,.],.],[.,[.,[.,.]]]]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 6
[[1,3,4,5],[2],[6]]
 => [6,2,1,3,4,5] => [[[.,.],.],[.,[.,[.,.]]]]
 => [1,1,1,0,0,0,1,0,1,0,1,0]
 => ? = 6
[[1,6],[2],[3],[4],[5]]
 => [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] => [[[[[.,.],.],.],.],[.,.]]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1
[[1,4],[2],[3],[5],[6]]
 => [6,5,3,2,1,4] => [[[[[.,.],.],.],.],[.,.]]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1
[[1,3],[2],[4],[5],[6]]
 => [6,5,4,2,1,3] => [[[[[.,.],.],.],.],[.,.]]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1
[[1,2],[3],[4],[5],[6]]
 => [6,5,4,3,1,2] => [[[[[.,.],.],.],.],[.,.]]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => 1
[[1],[2],[3],[4],[5],[6]]
 => [6,5,4,3,2,1] => [[[[[[.,.],.],.],.],.],.]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => 0
[[1,7],[2],[3],[4],[5],[6]]
 => [6,5,4,3,2,1,7] => [[[[[[.,.],.],.],.],.],[.,.]]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => 1
[[1,6],[2],[3],[4],[5],[7]]
 => [7,5,4,3,2,1,6] => [[[[[[.,.],.],.],.],.],[.,.]]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => 1
[[1,5],[2],[3],[4],[6],[7]]
 => [7,6,4,3,2,1,5] => [[[[[[.,.],.],.],.],.],[.,.]]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => 1
[[1,4],[2],[3],[5],[6],[7]]
 => [7,6,5,3,2,1,4] => [[[[[[.,.],.],.],.],.],[.,.]]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => 1
[[1,3],[2],[4],[5],[6],[7]]
 => [7,6,5,4,2,1,3] => [[[[[[.,.],.],.],.],.],[.,.]]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => 1
[[1,2],[3],[4],[5],[6],[7]]
 => [7,6,5,4,3,1,2] => [[[[[[.,.],.],.],.],.],[.,.]]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => 1
[[1],[2],[3],[4],[5],[6],[7]]
 => [7,6,5,4,3,2,1] => [[[[[[[.,.],.],.],.],.],.],.]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => 0
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.