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Matching statistic: St000572
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St000572: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
=> 0
{{1},{2}}
=> 0
{{1,2,3}}
=> 0
{{1,2},{3}}
=> 0
{{1,3},{2}}
=> 1
{{1},{2,3}}
=> 0
{{1},{2},{3}}
=> 0
{{1,2,3,4}}
=> 0
{{1,2,3},{4}}
=> 0
{{1,2,4},{3}}
=> 1
{{1,2},{3,4}}
=> 0
{{1,2},{3},{4}}
=> 0
{{1,3,4},{2}}
=> 1
{{1,3},{2,4}}
=> 2
{{1,3},{2},{4}}
=> 1
{{1,4},{2,3}}
=> 2
{{1},{2,3,4}}
=> 0
{{1},{2,3},{4}}
=> 0
{{1,4},{2},{3}}
=> 2
{{1},{2,4},{3}}
=> 1
{{1},{2},{3,4}}
=> 0
{{1},{2},{3},{4}}
=> 0
{{1,2,3,4,5}}
=> 0
{{1,2,3,4},{5}}
=> 0
{{1,2,3,5},{4}}
=> 1
{{1,2,3},{4,5}}
=> 0
{{1,2,3},{4},{5}}
=> 0
{{1,2,4,5},{3}}
=> 1
{{1,2,4},{3,5}}
=> 2
{{1,2,4},{3},{5}}
=> 1
{{1,2,5},{3,4}}
=> 2
{{1,2},{3,4,5}}
=> 0
{{1,2},{3,4},{5}}
=> 0
{{1,2,5},{3},{4}}
=> 2
{{1,2},{3,5},{4}}
=> 1
{{1,2},{3},{4,5}}
=> 0
{{1,2},{3},{4},{5}}
=> 0
{{1,3,4,5},{2}}
=> 1
{{1,3,4},{2,5}}
=> 3
{{1,3,4},{2},{5}}
=> 1
{{1,3,5},{2,4}}
=> 3
{{1,3},{2,4,5}}
=> 2
{{1,3},{2,4},{5}}
=> 2
{{1,3,5},{2},{4}}
=> 2
{{1,3},{2,5},{4}}
=> 3
{{1,3},{2},{4,5}}
=> 1
{{1,3},{2},{4},{5}}
=> 1
{{1,4,5},{2,3}}
=> 2
{{1,4},{2,3,5}}
=> 3
{{1,4},{2,3},{5}}
=> 2
Description
The dimension exponent of a set partition.
This is
$$\sum_{B\in\pi} (\max(B) - \min(B) + 1) - n$$
where the summation runs over the blocks of the set partition $\pi$ of $\{1,\dots,n\}$.
It is thus equal to the difference [[St000728]] - [[St000211]].
This is also the number of occurrences of the pattern {{1, 3}, {2}}, such that 1 and 3 are consecutive elements in a block.
This is also the number of occurrences of the pattern {{1, 3}, {2}}, such that 1 is the minimal and 3 is the maximal element of the block.
Matching statistic: St001596
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
St001596: Skew partitions ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 30%
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00233: Dyck paths —skew partition⟶ Skew partitions
St001596: Skew partitions ⟶ ℤResult quality: 16% ●values known / values provided: 16%●distinct values known / distinct values provided: 30%
Values
{{1,2}}
=> [2,1] => [1,1,0,0]
=> [[2],[]]
=> 0
{{1},{2}}
=> [1,2] => [1,0,1,0]
=> [[1,1],[]]
=> 0
{{1,2,3}}
=> [2,3,1] => [1,1,0,1,0,0]
=> [[3],[]]
=> 0
{{1,2},{3}}
=> [2,1,3] => [1,1,0,0,1,0]
=> [[2,2],[1]]
=> 0
{{1,3},{2}}
=> [3,2,1] => [1,1,1,0,0,0]
=> [[2,2],[]]
=> 1
{{1},{2,3}}
=> [1,3,2] => [1,0,1,1,0,0]
=> [[2,1],[]]
=> 0
{{1},{2},{3}}
=> [1,2,3] => [1,0,1,0,1,0]
=> [[1,1,1],[]]
=> 0
{{1,2,3,4}}
=> [2,3,4,1] => [1,1,0,1,0,1,0,0]
=> [[4],[]]
=> 0
{{1,2,3},{4}}
=> [2,3,1,4] => [1,1,0,1,0,0,1,0]
=> [[3,3],[2]]
=> 0
{{1,2,4},{3}}
=> [2,4,3,1] => [1,1,0,1,1,0,0,0]
=> [[3,3],[1]]
=> 1
{{1,2},{3,4}}
=> [2,1,4,3] => [1,1,0,0,1,1,0,0]
=> [[3,2],[1]]
=> 0
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,1,0,0,1,0,1,0]
=> [[2,2,2],[1,1]]
=> 0
{{1,3,4},{2}}
=> [3,2,4,1] => [1,1,1,0,0,1,0,0]
=> [[3,2],[]]
=> 1
{{1,3},{2,4}}
=> [3,4,1,2] => [1,1,1,0,1,0,0,0]
=> [[2,2,2],[]]
=> 2
{{1,3},{2},{4}}
=> [3,2,1,4] => [1,1,1,0,0,0,1,0]
=> [[2,2,2],[1]]
=> 1
{{1,4},{2,3}}
=> [4,3,2,1] => [1,1,1,1,0,0,0,0]
=> [[3,3],[]]
=> 2
{{1},{2,3,4}}
=> [1,3,4,2] => [1,0,1,1,0,1,0,0]
=> [[3,1],[]]
=> 0
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,0,1,1,0,0,1,0]
=> [[2,2,1],[1]]
=> 0
{{1,4},{2},{3}}
=> [4,2,3,1] => [1,1,1,1,0,0,0,0]
=> [[3,3],[]]
=> 2
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,0,1,1,1,0,0,0]
=> [[2,2,1],[]]
=> 1
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,0,1,0,1,1,0,0]
=> [[2,1,1],[]]
=> 0
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,0,1,0,1,0,1,0]
=> [[1,1,1,1],[]]
=> 0
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0]
=> [[5],[]]
=> 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0]
=> [[4,4],[3]]
=> 0
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0]
=> [[4,4],[2]]
=> 1
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0]
=> [[4,3],[2]]
=> 0
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0]
=> [[3,3,3],[2,2]]
=> 0
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0]
=> [[4,3],[1]]
=> 1
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0]
=> [[3,3,3],[1,1]]
=> 2
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0]
=> [[3,3,3],[2,1]]
=> 1
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,1,0,1,1,1,0,0,0,0]
=> [[4,4],[1]]
=> 2
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0]
=> [[4,2],[1]]
=> 0
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
=> [[3,3,2],[2,1]]
=> 0
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,1,0,1,1,1,0,0,0,0]
=> [[4,4],[1]]
=> 2
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0]
=> [[3,3,2],[1,1]]
=> 1
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
=> [[3,2,2],[1,1]]
=> 0
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
=> [[2,2,2,2],[1,1,1]]
=> 0
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0]
=> [[4,2],[]]
=> 1
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [1,1,1,0,1,1,0,0,0,0]
=> [[3,3,2],[]]
=> ? = 3
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0]
=> [[3,3,2],[2]]
=> 1
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0]
=> [[2,2,2,2],[]]
=> ? = 3
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0]
=> [[3,2,2],[]]
=> 2
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0]
=> [[2,2,2,2],[1]]
=> 2
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0]
=> [[3,3,2],[1]]
=> 2
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [1,1,1,0,1,1,0,0,0,0]
=> [[3,3,2],[]]
=> ? = 3
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0]
=> [[3,2,2],[1]]
=> 1
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,1,1,0,0,0,1,0,1,0]
=> [[2,2,2,2],[1,1]]
=> 1
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [1,1,1,1,0,0,0,1,0,0]
=> [[4,3],[]]
=> 2
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [1,1,1,1,0,0,1,0,0,0]
=> [[3,3,3],[1]]
=> ? = 3
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [1,1,1,1,0,0,0,0,1,0]
=> [[3,3,3],[2]]
=> 2
{{1,5},{2,3,4}}
=> [5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3],[]]
=> ? = 3
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
=> [[4,1],[]]
=> 0
{{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
=> [[3,3,1],[2]]
=> 0
{{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3],[]]
=> ? = 3
{{1},{2,3,5},{4}}
=> [1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
=> [[3,3,1],[1]]
=> 1
{{1},{2,3},{4,5}}
=> [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
=> [[3,2,1],[1]]
=> 0
{{1,4},{2,5},{3}}
=> [4,5,3,1,2] => [1,1,1,1,0,1,0,0,0,0]
=> [[4,4],[]]
=> ? = 4
{{1,4},{2},{3,5}}
=> [4,2,5,1,3] => [1,1,1,1,0,0,1,0,0,0]
=> [[3,3,3],[1]]
=> ? = 3
{{1,5},{2,4},{3}}
=> [5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3],[]]
=> ? = 4
{{1,5},{2},{3,4}}
=> [5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3],[]]
=> ? = 3
{{1,5},{2},{3},{4}}
=> [5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
=> [[3,3,3],[]]
=> ? = 3
{{1,2,3,5},{4,6}}
=> [2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0]
=> [[4,4,4],[2,2]]
=> ? = 2
{{1,2,3,6},{4,5}}
=> [2,3,6,5,4,1] => [1,1,0,1,0,1,1,1,0,0,0,0]
=> [[5,5],[2]]
=> ? = 2
{{1,2,3,6},{4},{5}}
=> [2,3,6,4,5,1] => [1,1,0,1,0,1,1,1,0,0,0,0]
=> [[5,5],[2]]
=> ? = 2
{{1,2,4,5},{3,6}}
=> [2,4,6,5,1,3] => [1,1,0,1,1,0,1,1,0,0,0,0]
=> [[4,4,3],[1,1]]
=> ? = 3
{{1,2,4,6},{3,5}}
=> [2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0]
=> [[3,3,3,3],[1,1,1]]
=> ? = 3
{{1,2,4},{3,5,6}}
=> [2,4,5,1,6,3] => [1,1,0,1,1,0,1,0,0,1,0,0]
=> [[4,3,3],[1,1]]
=> ? = 2
{{1,2,4},{3,5},{6}}
=> [2,4,5,1,3,6] => [1,1,0,1,1,0,1,0,0,0,1,0]
=> [[3,3,3,3],[2,1,1]]
=> ? = 2
{{1,2,4,6},{3},{5}}
=> [2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0]
=> [[4,4,3],[2,1]]
=> ? = 2
{{1,2,4},{3,6},{5}}
=> [2,4,6,1,5,3] => [1,1,0,1,1,0,1,1,0,0,0,0]
=> [[4,4,3],[1,1]]
=> ? = 3
{{1,2,5,6},{3,4}}
=> [2,5,4,3,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0]
=> [[5,4],[1]]
=> ? = 2
{{1,2,5},{3,4,6}}
=> [2,5,4,6,1,3] => [1,1,0,1,1,1,0,0,1,0,0,0]
=> [[4,4,4],[2,1]]
=> ? = 3
{{1,2,5},{3,4},{6}}
=> [2,5,4,3,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0]
=> [[4,4,4],[3,1]]
=> ? = 2
{{1,2,6},{3,4,5}}
=> [2,6,4,5,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0]
=> [[4,4,4],[1,1]]
=> ? = 3
{{1,2,6},{3,4},{5}}
=> [2,6,4,3,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0]
=> [[4,4,4],[1,1]]
=> ? = 3
{{1,2,5,6},{3},{4}}
=> [2,5,3,4,6,1] => [1,1,0,1,1,1,0,0,0,1,0,0]
=> [[5,4],[1]]
=> ? = 2
{{1,2,5},{3,6},{4}}
=> [2,5,6,4,1,3] => [1,1,0,1,1,1,0,1,0,0,0,0]
=> [[5,5],[1]]
=> ? = 4
{{1,2,5},{3},{4,6}}
=> [2,5,3,6,1,4] => [1,1,0,1,1,1,0,0,1,0,0,0]
=> [[4,4,4],[2,1]]
=> ? = 3
{{1,2,5},{3},{4},{6}}
=> [2,5,3,4,1,6] => [1,1,0,1,1,1,0,0,0,0,1,0]
=> [[4,4,4],[3,1]]
=> ? = 2
{{1,2,6},{3,5},{4}}
=> [2,6,5,4,3,1] => [1,1,0,1,1,1,1,0,0,0,0,0]
=> [[4,4,4],[1,1]]
=> ? = 4
{{1,2},{3,5},{4,6}}
=> [2,1,5,6,3,4] => [1,1,0,0,1,1,1,0,1,0,0,0]
=> [[3,3,3,2],[1,1,1]]
=> ? = 2
{{1,2,6},{3},{4,5}}
=> [2,6,3,5,4,1] => [1,1,0,1,1,1,1,0,0,0,0,0]
=> [[4,4,4],[1,1]]
=> ? = 3
{{1,2},{3,6},{4,5}}
=> [2,1,6,5,4,3] => [1,1,0,0,1,1,1,1,0,0,0,0]
=> [[4,4,2],[1,1]]
=> ? = 2
{{1,2,6},{3},{4},{5}}
=> [2,6,3,4,5,1] => [1,1,0,1,1,1,1,0,0,0,0,0]
=> [[4,4,4],[1,1]]
=> ? = 3
{{1,2},{3,6},{4},{5}}
=> [2,1,6,4,5,3] => [1,1,0,0,1,1,1,1,0,0,0,0]
=> [[4,4,2],[1,1]]
=> ? = 2
{{1,3,4,5},{2,6}}
=> [3,6,4,5,1,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
=> [[3,3,3,2],[]]
=> ? = 4
{{1,3,4,6},{2,5}}
=> [3,5,4,6,2,1] => [1,1,1,0,1,1,0,0,1,0,0,0]
=> [[3,3,3,2],[1]]
=> ? = 4
{{1,3,4},{2,5,6}}
=> [3,5,4,1,6,2] => [1,1,1,0,1,1,0,0,0,1,0,0]
=> [[4,3,2],[]]
=> ? = 3
{{1,3,4},{2,5},{6}}
=> [3,5,4,1,2,6] => [1,1,1,0,1,1,0,0,0,0,1,0]
=> [[3,3,3,2],[2]]
=> ? = 3
{{1,3,4,6},{2},{5}}
=> [3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0]
=> [[4,4,2],[2]]
=> ? = 2
{{1,3,4},{2,6},{5}}
=> [3,6,4,1,5,2] => [1,1,1,0,1,1,1,0,0,0,0,0]
=> [[3,3,3,2],[]]
=> ? = 4
{{1,3,5,6},{2,4}}
=> [3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0]
=> [[3,2,2,2],[]]
=> ? = 3
{{1,3,5},{2,4,6}}
=> [3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0]
=> [[2,2,2,2,2],[]]
=> ? = 4
{{1,3,5},{2,4},{6}}
=> [3,4,5,2,1,6] => [1,1,1,0,1,0,1,0,0,0,1,0]
=> [[2,2,2,2,2],[1]]
=> ? = 3
{{1,3,6},{2,4,5}}
=> [3,4,6,5,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0]
=> [[3,3,2,2],[]]
=> ? = 4
{{1,3},{2,4,5,6}}
=> [3,4,1,5,6,2] => [1,1,1,0,1,0,0,1,0,1,0,0]
=> [[4,2,2],[]]
=> ? = 2
{{1,3},{2,4,5},{6}}
=> [3,4,1,5,2,6] => [1,1,1,0,1,0,0,1,0,0,1,0]
=> [[3,3,2,2],[2]]
=> ? = 2
{{1,3,6},{2,4},{5}}
=> [3,4,6,2,5,1] => [1,1,1,0,1,0,1,1,0,0,0,0]
=> [[3,3,2,2],[]]
=> ? = 4
{{1,3},{2,4,6},{5}}
=> [3,4,1,6,5,2] => [1,1,1,0,1,0,0,1,1,0,0,0]
=> [[3,3,2,2],[1]]
=> ? = 3
{{1,3},{2,4},{5,6}}
=> [3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0]
=> [[3,2,2,2],[1]]
=> ? = 2
Description
The number of two-by-two squares inside a skew partition.
This is, the number of cells $(i,j)$ in a skew partition for which the box $(i+1,j+1)$ is also a cell inside the skew partition.
Matching statistic: St001207
Mp00215: Set partitions —Wachs-White⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 30%
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 30%
Values
{{1,2}}
=> {{1,2}}
=> [2,1] => [1,2] => 0
{{1},{2}}
=> {{1},{2}}
=> [1,2] => [1,2] => 0
{{1,2,3}}
=> {{1,2,3}}
=> [2,3,1] => [1,2,3] => 0
{{1,2},{3}}
=> {{1},{2,3}}
=> [1,3,2] => [1,2,3] => 0
{{1,3},{2}}
=> {{1,3},{2}}
=> [3,2,1] => [1,3,2] => 1
{{1},{2,3}}
=> {{1,2},{3}}
=> [2,1,3] => [1,2,3] => 0
{{1},{2},{3}}
=> {{1},{2},{3}}
=> [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
=> {{1,2,3,4}}
=> [2,3,4,1] => [1,2,3,4] => 0
{{1,2,3},{4}}
=> {{1},{2,3,4}}
=> [1,3,4,2] => [1,2,3,4] => 0
{{1,2,4},{3}}
=> {{1,3},{2,4}}
=> [3,4,1,2] => [1,3,2,4] => 1
{{1,2},{3,4}}
=> {{1,2},{3,4}}
=> [2,1,4,3] => [1,2,3,4] => 0
{{1,2},{3},{4}}
=> {{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,3,4] => 0
{{1,3,4},{2}}
=> {{1,2,4},{3}}
=> [2,4,3,1] => [1,2,4,3] => 1
{{1,3},{2,4}}
=> {{1,3,4},{2}}
=> [3,2,4,1] => [1,3,4,2] => 2
{{1,3},{2},{4}}
=> {{1},{2,4},{3}}
=> [1,4,3,2] => [1,2,4,3] => 1
{{1,4},{2,3}}
=> {{1,4},{2,3}}
=> [4,3,2,1] => [1,4,2,3] => 2
{{1},{2,3,4}}
=> {{1,2,3},{4}}
=> [2,3,1,4] => [1,2,3,4] => 0
{{1},{2,3},{4}}
=> {{1},{2,3},{4}}
=> [1,3,2,4] => [1,2,3,4] => 0
{{1,4},{2},{3}}
=> {{1,4},{2},{3}}
=> [4,2,3,1] => [1,4,2,3] => 2
{{1},{2,4},{3}}
=> {{1,3},{2},{4}}
=> [3,2,1,4] => [1,3,2,4] => 1
{{1},{2},{3,4}}
=> {{1,2},{3},{4}}
=> [2,1,3,4] => [1,2,3,4] => 0
{{1},{2},{3},{4}}
=> {{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}}
=> {{1,2,3,4,5}}
=> [2,3,4,5,1] => [1,2,3,4,5] => ? = 0
{{1,2,3,4},{5}}
=> {{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,2,3,4,5] => ? = 0
{{1,2,3,5},{4}}
=> {{1,3},{2,4,5}}
=> [3,4,1,5,2] => [1,3,2,4,5] => ? = 1
{{1,2,3},{4,5}}
=> {{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
{{1,2,3},{4},{5}}
=> {{1},{2},{3,4,5}}
=> [1,2,4,5,3] => [1,2,3,4,5] => ? = 0
{{1,2,4,5},{3}}
=> {{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,2,4,3,5] => ? = 1
{{1,2,4},{3,5}}
=> {{1,3,4},{2,5}}
=> [3,5,4,1,2] => [1,3,4,2,5] => ? = 2
{{1,2,4},{3},{5}}
=> {{1},{2,4},{3,5}}
=> [1,4,5,2,3] => [1,2,4,3,5] => ? = 1
{{1,2,5},{3,4}}
=> {{1,4},{2,3,5}}
=> [4,3,5,1,2] => [1,4,2,3,5] => ? = 2
{{1,2},{3,4,5}}
=> {{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,2,3,4,5] => ? = 0
{{1,2},{3,4},{5}}
=> {{1},{2,3},{4,5}}
=> [1,3,2,5,4] => [1,2,3,4,5] => ? = 0
{{1,2,5},{3},{4}}
=> {{1,4},{2},{3,5}}
=> [4,2,5,1,3] => [1,4,2,3,5] => ? = 2
{{1,2},{3,5},{4}}
=> {{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [1,3,2,4,5] => ? = 1
{{1,2},{3},{4,5}}
=> {{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,2,3,4,5] => ? = 0
{{1,2},{3},{4},{5}}
=> {{1},{2},{3},{4,5}}
=> [1,2,3,5,4] => [1,2,3,4,5] => ? = 0
{{1,3,4,5},{2}}
=> {{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,2,3,5,4] => ? = 1
{{1,3,4},{2,5}}
=> {{1,4,5},{2,3}}
=> [4,3,2,5,1] => [1,4,5,2,3] => ? = 3
{{1,3,4},{2},{5}}
=> {{1},{2,3,5},{4}}
=> [1,3,5,4,2] => [1,2,3,5,4] => ? = 1
{{1,3,5},{2,4}}
=> {{1,3,4,5},{2}}
=> [3,2,4,5,1] => [1,3,4,5,2] => ? = 3
{{1,3},{2,4,5}}
=> {{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,2,4,5,3] => ? = 2
{{1,3},{2,4},{5}}
=> {{1},{2,4,5},{3}}
=> [1,4,3,5,2] => [1,2,4,5,3] => ? = 2
{{1,3,5},{2},{4}}
=> {{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [1,3,2,5,4] => ? = 2
{{1,3},{2,5},{4}}
=> {{1,4},{2,5},{3}}
=> [4,5,3,1,2] => [1,4,2,5,3] => ? = 3
{{1,3},{2},{4,5}}
=> {{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,2,3,5,4] => ? = 1
{{1,3},{2},{4},{5}}
=> {{1},{2},{3,5},{4}}
=> [1,2,5,4,3] => [1,2,3,5,4] => ? = 1
{{1,4,5},{2,3}}
=> {{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,2,5,3,4] => ? = 2
{{1,4},{2,3,5}}
=> {{1,3,5},{2,4}}
=> [3,4,5,2,1] => [1,3,5,2,4] => ? = 3
{{1,4},{2,3},{5}}
=> {{1},{2,5},{3,4}}
=> [1,5,4,3,2] => [1,2,5,3,4] => ? = 2
{{1,5},{2,3,4}}
=> {{1,5},{2,3,4}}
=> [5,3,4,2,1] => [1,5,2,3,4] => ? = 3
{{1},{2,3,4,5}}
=> {{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,2,3,4,5] => ? = 0
{{1},{2,3,4},{5}}
=> {{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [1,2,3,4,5] => ? = 0
{{1,5},{2,3},{4}}
=> {{1,5},{2},{3,4}}
=> [5,2,4,3,1] => [1,5,2,3,4] => ? = 3
{{1},{2,3,5},{4}}
=> {{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [1,3,2,4,5] => ? = 1
{{1},{2,3},{4,5}}
=> {{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,2,3,4,5] => ? = 0
{{1},{2,3},{4},{5}}
=> {{1},{2},{3,4},{5}}
=> [1,2,4,3,5] => [1,2,3,4,5] => ? = 0
{{1,4,5},{2},{3}}
=> {{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,2,5,3,4] => ? = 2
{{1,4},{2,5},{3}}
=> {{1,4,5},{2},{3}}
=> [4,2,3,5,1] => [1,4,5,2,3] => ? = 4
{{1,4},{2},{3,5}}
=> {{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [1,3,5,2,4] => ? = 3
{{1,4},{2},{3},{5}}
=> {{1},{2,5},{3},{4}}
=> [1,5,3,4,2] => [1,2,5,3,4] => ? = 2
{{1,5},{2,4},{3}}
=> {{1,5},{2,4},{3}}
=> [5,4,3,2,1] => [1,5,2,4,3] => ? = 4
{{1},{2,4,5},{3}}
=> {{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,2,4,3,5] => ? = 1
{{1},{2,4},{3,5}}
=> {{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,3,4,2,5] => ? = 2
{{1},{2,4},{3},{5}}
=> {{1},{2,4},{3},{5}}
=> [1,4,3,2,5] => [1,2,4,3,5] => ? = 1
{{1,5},{2},{3,4}}
=> {{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [1,5,2,3,4] => ? = 3
{{1},{2,5},{3,4}}
=> {{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [1,4,2,3,5] => ? = 2
{{1},{2},{3,4,5}}
=> {{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,2,3,4,5] => ? = 0
{{1},{2},{3,4},{5}}
=> {{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => [1,2,3,4,5] => ? = 0
{{1,5},{2},{3},{4}}
=> {{1,5},{2},{3},{4}}
=> [5,2,3,4,1] => [1,5,2,3,4] => ? = 3
{{1},{2,5},{3},{4}}
=> {{1,4},{2},{3},{5}}
=> [4,2,3,1,5] => [1,4,2,3,5] => ? = 2
{{1},{2},{3,5},{4}}
=> {{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,3,2,4,5] => ? = 1
Description
The Lowey length of the algebra $A/T$ when $T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$.
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