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Your data matches 4 different statistics following compositions of up to 3 maps.
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Matching statistic: St000668
Mp00108: Permutations —cycle type⟶ Integer partitions
St000668: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000668: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [1,1]
=> 1
[2,1] => [2]
=> 2
[1,2,3] => [1,1,1]
=> 1
[1,3,2] => [2,1]
=> 2
[2,1,3] => [2,1]
=> 2
[2,3,1] => [3]
=> 3
[3,1,2] => [3]
=> 3
[3,2,1] => [2,1]
=> 2
[1,2,3,4] => [1,1,1,1]
=> 1
[1,2,4,3] => [2,1,1]
=> 2
[1,3,2,4] => [2,1,1]
=> 2
[1,3,4,2] => [3,1]
=> 3
[1,4,2,3] => [3,1]
=> 3
[1,4,3,2] => [2,1,1]
=> 2
[2,1,3,4] => [2,1,1]
=> 2
[2,1,4,3] => [2,2]
=> 2
[2,3,1,4] => [3,1]
=> 3
[2,3,4,1] => [4]
=> 4
[2,4,1,3] => [4]
=> 4
[2,4,3,1] => [3,1]
=> 3
[3,1,2,4] => [3,1]
=> 3
[3,1,4,2] => [4]
=> 4
[3,2,1,4] => [2,1,1]
=> 2
[3,2,4,1] => [3,1]
=> 3
[3,4,1,2] => [2,2]
=> 2
[3,4,2,1] => [4]
=> 4
[4,1,2,3] => [4]
=> 4
[4,1,3,2] => [3,1]
=> 3
[4,2,1,3] => [3,1]
=> 3
[4,2,3,1] => [2,1,1]
=> 2
[4,3,1,2] => [4]
=> 4
[4,3,2,1] => [2,2]
=> 2
[1,2,3,4,5] => [1,1,1,1,1]
=> 1
[1,2,3,5,4] => [2,1,1,1]
=> 2
[1,2,4,3,5] => [2,1,1,1]
=> 2
[1,2,4,5,3] => [3,1,1]
=> 3
[1,2,5,3,4] => [3,1,1]
=> 3
[1,2,5,4,3] => [2,1,1,1]
=> 2
[1,3,2,4,5] => [2,1,1,1]
=> 2
[1,3,2,5,4] => [2,2,1]
=> 2
[1,3,4,2,5] => [3,1,1]
=> 3
[1,3,4,5,2] => [4,1]
=> 4
[1,3,5,2,4] => [4,1]
=> 4
[1,3,5,4,2] => [3,1,1]
=> 3
[1,4,2,3,5] => [3,1,1]
=> 3
[1,4,2,5,3] => [4,1]
=> 4
[1,4,3,2,5] => [2,1,1,1]
=> 2
[1,4,3,5,2] => [3,1,1]
=> 3
[1,4,5,2,3] => [2,2,1]
=> 2
[1,4,5,3,2] => [4,1]
=> 4
Description
The least common multiple of the parts of the partition.
Matching statistic: St000058
(load all 14 compositions to match this statistic)
(load all 14 compositions to match this statistic)
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
St000058: Permutations ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 39%
Mp00080: Set partitions —to permutation⟶ Permutations
St000058: Permutations ⟶ ℤResult quality: 12% ●values known / values provided: 12%●distinct values known / distinct values provided: 39%
Values
[1,2] => {{1},{2}}
=> [1,2] => 1
[2,1] => {{1,2}}
=> [2,1] => 2
[1,2,3] => {{1},{2},{3}}
=> [1,2,3] => 1
[1,3,2] => {{1},{2,3}}
=> [1,3,2] => 2
[2,1,3] => {{1,2},{3}}
=> [2,1,3] => 2
[2,3,1] => {{1,2,3}}
=> [2,3,1] => 3
[3,1,2] => {{1,2,3}}
=> [2,3,1] => 3
[3,2,1] => {{1,3},{2}}
=> [3,2,1] => 2
[1,2,3,4] => {{1},{2},{3},{4}}
=> [1,2,3,4] => 1
[1,2,4,3] => {{1},{2},{3,4}}
=> [1,2,4,3] => 2
[1,3,2,4] => {{1},{2,3},{4}}
=> [1,3,2,4] => 2
[1,3,4,2] => {{1},{2,3,4}}
=> [1,3,4,2] => 3
[1,4,2,3] => {{1},{2,3,4}}
=> [1,3,4,2] => 3
[1,4,3,2] => {{1},{2,4},{3}}
=> [1,4,3,2] => 2
[2,1,3,4] => {{1,2},{3},{4}}
=> [2,1,3,4] => 2
[2,1,4,3] => {{1,2},{3,4}}
=> [2,1,4,3] => 2
[2,3,1,4] => {{1,2,3},{4}}
=> [2,3,1,4] => 3
[2,3,4,1] => {{1,2,3,4}}
=> [2,3,4,1] => 4
[2,4,1,3] => {{1,2,3,4}}
=> [2,3,4,1] => 4
[2,4,3,1] => {{1,2,4},{3}}
=> [2,4,3,1] => 3
[3,1,2,4] => {{1,2,3},{4}}
=> [2,3,1,4] => 3
[3,1,4,2] => {{1,2,3,4}}
=> [2,3,4,1] => 4
[3,2,1,4] => {{1,3},{2},{4}}
=> [3,2,1,4] => 2
[3,2,4,1] => {{1,3,4},{2}}
=> [3,2,4,1] => 3
[3,4,1,2] => {{1,3},{2,4}}
=> [3,4,1,2] => 2
[3,4,2,1] => {{1,2,3,4}}
=> [2,3,4,1] => 4
[4,1,2,3] => {{1,2,3,4}}
=> [2,3,4,1] => 4
[4,1,3,2] => {{1,2,4},{3}}
=> [2,4,3,1] => 3
[4,2,1,3] => {{1,3,4},{2}}
=> [3,2,4,1] => 3
[4,2,3,1] => {{1,4},{2},{3}}
=> [4,2,3,1] => 2
[4,3,1,2] => {{1,2,3,4}}
=> [2,3,4,1] => 4
[4,3,2,1] => {{1,4},{2,3}}
=> [4,3,2,1] => 2
[1,2,3,4,5] => {{1},{2},{3},{4},{5}}
=> [1,2,3,4,5] => 1
[1,2,3,5,4] => {{1},{2},{3},{4,5}}
=> [1,2,3,5,4] => 2
[1,2,4,3,5] => {{1},{2},{3,4},{5}}
=> [1,2,4,3,5] => 2
[1,2,4,5,3] => {{1},{2},{3,4,5}}
=> [1,2,4,5,3] => 3
[1,2,5,3,4] => {{1},{2},{3,4,5}}
=> [1,2,4,5,3] => 3
[1,2,5,4,3] => {{1},{2},{3,5},{4}}
=> [1,2,5,4,3] => 2
[1,3,2,4,5] => {{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => 2
[1,3,2,5,4] => {{1},{2,3},{4,5}}
=> [1,3,2,5,4] => 2
[1,3,4,2,5] => {{1},{2,3,4},{5}}
=> [1,3,4,2,5] => 3
[1,3,4,5,2] => {{1},{2,3,4,5}}
=> [1,3,4,5,2] => 4
[1,3,5,2,4] => {{1},{2,3,4,5}}
=> [1,3,4,5,2] => 4
[1,3,5,4,2] => {{1},{2,3,5},{4}}
=> [1,3,5,4,2] => 3
[1,4,2,3,5] => {{1},{2,3,4},{5}}
=> [1,3,4,2,5] => 3
[1,4,2,5,3] => {{1},{2,3,4,5}}
=> [1,3,4,5,2] => 4
[1,4,3,2,5] => {{1},{2,4},{3},{5}}
=> [1,4,3,2,5] => 2
[1,4,3,5,2] => {{1},{2,4,5},{3}}
=> [1,4,3,5,2] => 3
[1,4,5,2,3] => {{1},{2,4},{3,5}}
=> [1,4,5,2,3] => 2
[1,4,5,3,2] => {{1},{2,3,4,5}}
=> [1,3,4,5,2] => 4
[1,2,3,6,5,4,7] => {{1},{2},{3},{4,6},{5},{7}}
=> [1,2,3,6,5,4,7] => ? = 2
[1,2,3,6,5,7,4] => {{1},{2},{3},{4,6,7},{5}}
=> [1,2,3,6,5,7,4] => ? = 3
[1,2,3,7,5,4,6] => {{1},{2},{3},{4,6,7},{5}}
=> [1,2,3,6,5,7,4] => ? = 3
[1,2,4,6,5,3,7] => {{1},{2},{3,4,6},{5},{7}}
=> [1,2,4,6,5,3,7] => ? = 3
[1,2,4,6,5,7,3] => {{1},{2},{3,4,6,7},{5}}
=> [1,2,4,6,5,7,3] => ? = 4
[1,2,4,7,5,3,6] => {{1},{2},{3,4,6,7},{5}}
=> [1,2,4,6,5,7,3] => ? = 4
[1,2,5,4,3,6,7] => {{1},{2},{3,5},{4},{6},{7}}
=> [1,2,5,4,3,6,7] => ? = 2
[1,2,5,4,6,3,7] => {{1},{2},{3,5,6},{4},{7}}
=> [1,2,5,4,6,3,7] => ? = 3
[1,2,5,4,7,6,3] => {{1},{2},{3,5,7},{4},{6}}
=> [1,2,5,4,7,6,3] => ? = 3
[1,2,6,3,5,4,7] => {{1},{2},{3,4,6},{5},{7}}
=> [1,2,4,6,5,3,7] => ? = 3
[1,2,6,3,5,7,4] => {{1},{2},{3,4,6,7},{5}}
=> [1,2,4,6,5,7,3] => ? = 4
[1,2,6,4,3,5,7] => {{1},{2},{3,5,6},{4},{7}}
=> [1,2,5,4,6,3,7] => ? = 3
[1,2,6,4,5,3,7] => {{1},{2},{3,6},{4},{5},{7}}
=> [1,2,6,4,5,3,7] => ? = 2
[1,2,6,4,5,7,3] => {{1},{2},{3,6,7},{4},{5}}
=> [1,2,6,4,5,7,3] => ? = 3
[1,2,6,5,4,3,7] => {{1},{2},{3,6},{4,5},{7}}
=> [1,2,6,5,4,3,7] => ? = 2
[1,2,6,7,5,4,3] => {{1},{2},{3,4,6,7},{5}}
=> [1,2,4,6,5,7,3] => ? = 4
[1,2,7,3,5,4,6] => {{1},{2},{3,4,6,7},{5}}
=> [1,2,4,6,5,7,3] => ? = 4
[1,2,7,4,3,6,5] => {{1},{2},{3,5,7},{4},{6}}
=> [1,2,5,4,7,6,3] => ? = 3
[1,2,7,4,5,3,6] => {{1},{2},{3,6,7},{4},{5}}
=> [1,2,6,4,5,7,3] => ? = 3
[1,2,7,4,6,5,3] => {{1},{2},{3,7},{4},{5,6}}
=> [1,2,7,4,6,5,3] => ? = 2
[1,2,7,5,4,6,3] => {{1},{2},{3,7},{4,5},{6}}
=> [1,2,7,5,4,6,3] => ? = 2
[1,2,7,6,5,3,4] => {{1},{2},{3,4,6,7},{5}}
=> [1,2,4,6,5,7,3] => ? = 4
[1,3,2,5,7,6,4] => {{1},{2,3},{4,5,7},{6}}
=> [1,3,2,5,7,6,4] => ? = 6
[1,3,2,6,5,4,7] => {{1},{2,3},{4,6},{5},{7}}
=> [1,3,2,6,5,4,7] => ? = 2
[1,3,2,6,5,7,4] => {{1},{2,3},{4,6,7},{5}}
=> [1,3,2,6,5,7,4] => ? = 6
[1,3,2,7,4,6,5] => {{1},{2,3},{4,5,7},{6}}
=> [1,3,2,5,7,6,4] => ? = 6
[1,3,2,7,5,4,6] => {{1},{2,3},{4,6,7},{5}}
=> [1,3,2,6,5,7,4] => ? = 6
[1,3,2,7,5,6,4] => {{1},{2,3},{4,7},{5},{6}}
=> [1,3,2,7,5,6,4] => ? = 2
[1,3,2,7,6,5,4] => {{1},{2,3},{4,7},{5,6}}
=> [1,3,2,7,6,5,4] => ? = 2
[1,3,4,6,5,2,7] => {{1},{2,3,4,6},{5},{7}}
=> [1,3,4,6,5,2,7] => ? = 4
[1,3,4,6,5,7,2] => {{1},{2,3,4,6,7},{5}}
=> [1,3,4,6,5,7,2] => ? = 5
[1,3,4,7,5,2,6] => {{1},{2,3,4,6,7},{5}}
=> [1,3,4,6,5,7,2] => ? = 5
[1,3,5,4,2,6,7] => {{1},{2,3,5},{4},{6},{7}}
=> [1,3,5,4,2,6,7] => ? = 3
[1,3,5,4,2,7,6] => {{1},{2,3,5},{4},{6,7}}
=> [1,3,5,4,2,7,6] => ? = 6
[1,3,5,4,6,2,7] => {{1},{2,3,5,6},{4},{7}}
=> [1,3,5,4,6,2,7] => ? = 4
[1,3,5,4,6,7,2] => {{1},{2,3,5,6,7},{4}}
=> [1,3,5,4,6,7,2] => ? = 5
[1,3,5,4,7,2,6] => {{1},{2,3,5,6,7},{4}}
=> [1,3,5,4,6,7,2] => ? = 5
[1,3,5,4,7,6,2] => {{1},{2,3,5,7},{4},{6}}
=> [1,3,5,4,7,6,2] => ? = 4
[1,3,5,7,6,2,4] => {{1},{2,3,5,6},{4,7}}
=> [1,3,5,7,6,2,4] => ? = 4
[1,3,6,2,5,4,7] => {{1},{2,3,4,6},{5},{7}}
=> [1,3,4,6,5,2,7] => ? = 4
[1,3,6,2,5,7,4] => {{1},{2,3,4,6,7},{5}}
=> [1,3,4,6,5,7,2] => ? = 5
[1,3,6,4,2,5,7] => {{1},{2,3,5,6},{4},{7}}
=> [1,3,5,4,6,2,7] => ? = 4
[1,3,6,4,2,7,5] => {{1},{2,3,5,6,7},{4}}
=> [1,3,5,4,6,7,2] => ? = 5
[1,3,6,4,5,2,7] => {{1},{2,3,6},{4},{5},{7}}
=> [1,3,6,4,5,2,7] => ? = 3
[1,3,6,4,7,2,5] => {{1},{2,3,6},{4},{5,7}}
=> [1,3,6,4,7,2,5] => ? = 6
[1,3,6,4,7,5,2] => {{1},{2,3,5,6,7},{4}}
=> [1,3,5,4,6,7,2] => ? = 5
[1,3,6,5,4,2,7] => {{1},{2,3,6},{4,5},{7}}
=> [1,3,6,5,4,2,7] => ? = 6
[1,3,6,5,4,7,2] => {{1},{2,3,6,7},{4,5}}
=> [1,3,6,5,4,7,2] => ? = 4
[1,3,6,5,7,2,4] => {{1},{2,3,6},{4,5,7}}
=> [1,3,6,5,7,2,4] => ? = 3
[1,3,6,7,2,5,4] => {{1},{2,3,5,6},{4,7}}
=> [1,3,5,7,6,2,4] => ? = 4
Description
The order of a permutation.
ord(π) is given by the minimial k for which πk is the identity permutation.
Matching statistic: St001555
(load all 10 compositions to match this statistic)
(load all 10 compositions to match this statistic)
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001555: Signed permutations ⟶ ℤResult quality: 0% ●values known / values provided: 0%●distinct values known / distinct values provided: 26%
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001555: Signed permutations ⟶ ℤResult quality: 0% ●values known / values provided: 0%●distinct values known / distinct values provided: 26%
Values
[1,2] => {{1},{2}}
=> [1,2] => [1,2] => 1
[2,1] => {{1,2}}
=> [2,1] => [2,1] => 2
[1,2,3] => {{1},{2},{3}}
=> [1,2,3] => [1,2,3] => 1
[1,3,2] => {{1},{2,3}}
=> [1,3,2] => [1,3,2] => 2
[2,1,3] => {{1,2},{3}}
=> [2,1,3] => [2,1,3] => 2
[2,3,1] => {{1,2,3}}
=> [2,3,1] => [2,3,1] => 3
[3,1,2] => {{1,2,3}}
=> [2,3,1] => [2,3,1] => 3
[3,2,1] => {{1,3},{2}}
=> [3,2,1] => [3,2,1] => 2
[1,2,3,4] => {{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => 1
[1,2,4,3] => {{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,4,3] => 2
[1,3,2,4] => {{1},{2,3},{4}}
=> [1,3,2,4] => [1,3,2,4] => 2
[1,3,4,2] => {{1},{2,3,4}}
=> [1,3,4,2] => [1,3,4,2] => 3
[1,4,2,3] => {{1},{2,3,4}}
=> [1,3,4,2] => [1,3,4,2] => 3
[1,4,3,2] => {{1},{2,4},{3}}
=> [1,4,3,2] => [1,4,3,2] => 2
[2,1,3,4] => {{1,2},{3},{4}}
=> [2,1,3,4] => [2,1,3,4] => 2
[2,1,4,3] => {{1,2},{3,4}}
=> [2,1,4,3] => [2,1,4,3] => 2
[2,3,1,4] => {{1,2,3},{4}}
=> [2,3,1,4] => [2,3,1,4] => 3
[2,3,4,1] => {{1,2,3,4}}
=> [2,3,4,1] => [2,3,4,1] => 4
[2,4,1,3] => {{1,2,3,4}}
=> [2,3,4,1] => [2,3,4,1] => 4
[2,4,3,1] => {{1,2,4},{3}}
=> [2,4,3,1] => [2,4,3,1] => 3
[3,1,2,4] => {{1,2,3},{4}}
=> [2,3,1,4] => [2,3,1,4] => 3
[3,1,4,2] => {{1,2,3,4}}
=> [2,3,4,1] => [2,3,4,1] => 4
[3,2,1,4] => {{1,3},{2},{4}}
=> [3,2,1,4] => [3,2,1,4] => 2
[3,2,4,1] => {{1,3,4},{2}}
=> [3,2,4,1] => [3,2,4,1] => 3
[3,4,1,2] => {{1,3},{2,4}}
=> [3,4,1,2] => [3,4,1,2] => 2
[3,4,2,1] => {{1,2,3,4}}
=> [2,3,4,1] => [2,3,4,1] => 4
[4,1,2,3] => {{1,2,3,4}}
=> [2,3,4,1] => [2,3,4,1] => 4
[4,1,3,2] => {{1,2,4},{3}}
=> [2,4,3,1] => [2,4,3,1] => 3
[4,2,1,3] => {{1,3,4},{2}}
=> [3,2,4,1] => [3,2,4,1] => 3
[4,2,3,1] => {{1,4},{2},{3}}
=> [4,2,3,1] => [4,2,3,1] => 2
[4,3,1,2] => {{1,2,3,4}}
=> [2,3,4,1] => [2,3,4,1] => 4
[4,3,2,1] => {{1,4},{2,3}}
=> [4,3,2,1] => [4,3,2,1] => 2
[1,2,3,4,5] => {{1},{2},{3},{4},{5}}
=> [1,2,3,4,5] => [1,2,3,4,5] => 1
[1,2,3,5,4] => {{1},{2},{3},{4,5}}
=> [1,2,3,5,4] => [1,2,3,5,4] => 2
[1,2,4,3,5] => {{1},{2},{3,4},{5}}
=> [1,2,4,3,5] => [1,2,4,3,5] => 2
[1,2,4,5,3] => {{1},{2},{3,4,5}}
=> [1,2,4,5,3] => [1,2,4,5,3] => 3
[1,2,5,3,4] => {{1},{2},{3,4,5}}
=> [1,2,4,5,3] => [1,2,4,5,3] => 3
[1,2,5,4,3] => {{1},{2},{3,5},{4}}
=> [1,2,5,4,3] => [1,2,5,4,3] => 2
[1,3,2,4,5] => {{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => [1,3,2,4,5] => 2
[1,3,2,5,4] => {{1},{2,3},{4,5}}
=> [1,3,2,5,4] => [1,3,2,5,4] => 2
[1,3,4,2,5] => {{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [1,3,4,2,5] => 3
[1,3,4,5,2] => {{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,3,4,5,2] => 4
[1,3,5,2,4] => {{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,3,4,5,2] => 4
[1,3,5,4,2] => {{1},{2,3,5},{4}}
=> [1,3,5,4,2] => [1,3,5,4,2] => 3
[1,4,2,3,5] => {{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [1,3,4,2,5] => 3
[1,4,2,5,3] => {{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,3,4,5,2] => 4
[1,4,3,2,5] => {{1},{2,4},{3},{5}}
=> [1,4,3,2,5] => [1,4,3,2,5] => 2
[1,4,3,5,2] => {{1},{2,4,5},{3}}
=> [1,4,3,5,2] => [1,4,3,5,2] => 3
[1,4,5,2,3] => {{1},{2,4},{3,5}}
=> [1,4,5,2,3] => [1,4,5,2,3] => 2
[1,4,5,3,2] => {{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,3,4,5,2] => 4
[5,3,2,4,1] => {{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [5,3,2,4,1] => ? = 2
[5,3,4,2,1] => {{1,5},{2,3,4}}
=> [5,3,4,2,1] => [5,3,4,2,1] => ? = 6
[5,4,2,3,1] => {{1,5},{2,3,4}}
=> [5,3,4,2,1] => [5,3,4,2,1] => ? = 6
[5,4,3,2,1] => {{1,5},{2,4},{3}}
=> [5,4,3,2,1] => [5,4,3,2,1] => ? = 2
[1,2,3,4,5,6] => {{1},{2},{3},{4},{5},{6}}
=> [1,2,3,4,5,6] => [1,2,3,4,5,6] => ? = 1
[1,2,3,4,6,5] => {{1},{2},{3},{4},{5,6}}
=> [1,2,3,4,6,5] => [1,2,3,4,6,5] => ? = 2
[1,2,3,5,4,6] => {{1},{2},{3},{4,5},{6}}
=> [1,2,3,5,4,6] => [1,2,3,5,4,6] => ? = 2
[1,2,3,5,6,4] => {{1},{2},{3},{4,5,6}}
=> [1,2,3,5,6,4] => [1,2,3,5,6,4] => ? = 3
[1,2,3,6,4,5] => {{1},{2},{3},{4,5,6}}
=> [1,2,3,5,6,4] => [1,2,3,5,6,4] => ? = 3
[1,2,3,6,5,4] => {{1},{2},{3},{4,6},{5}}
=> [1,2,3,6,5,4] => [1,2,3,6,5,4] => ? = 2
[1,2,4,3,5,6] => {{1},{2},{3,4},{5},{6}}
=> [1,2,4,3,5,6] => [1,2,4,3,5,6] => ? = 2
[1,2,4,3,6,5] => {{1},{2},{3,4},{5,6}}
=> [1,2,4,3,6,5] => [1,2,4,3,6,5] => ? = 2
[1,2,4,5,3,6] => {{1},{2},{3,4,5},{6}}
=> [1,2,4,5,3,6] => [1,2,4,5,3,6] => ? = 3
[1,2,4,5,6,3] => {{1},{2},{3,4,5,6}}
=> [1,2,4,5,6,3] => [1,2,4,5,6,3] => ? = 4
[1,2,4,6,3,5] => {{1},{2},{3,4,5,6}}
=> [1,2,4,5,6,3] => [1,2,4,5,6,3] => ? = 4
[1,2,4,6,5,3] => {{1},{2},{3,4,6},{5}}
=> [1,2,4,6,5,3] => [1,2,4,6,5,3] => ? = 3
[1,2,5,3,4,6] => {{1},{2},{3,4,5},{6}}
=> [1,2,4,5,3,6] => [1,2,4,5,3,6] => ? = 3
[1,2,5,3,6,4] => {{1},{2},{3,4,5,6}}
=> [1,2,4,5,6,3] => [1,2,4,5,6,3] => ? = 4
[1,2,5,4,3,6] => {{1},{2},{3,5},{4},{6}}
=> [1,2,5,4,3,6] => [1,2,5,4,3,6] => ? = 2
[1,2,5,4,6,3] => {{1},{2},{3,5,6},{4}}
=> [1,2,5,4,6,3] => [1,2,5,4,6,3] => ? = 3
[1,2,5,6,3,4] => {{1},{2},{3,5},{4,6}}
=> [1,2,5,6,3,4] => [1,2,5,6,3,4] => ? = 2
[1,2,5,6,4,3] => {{1},{2},{3,4,5,6}}
=> [1,2,4,5,6,3] => [1,2,4,5,6,3] => ? = 4
[1,2,6,3,4,5] => {{1},{2},{3,4,5,6}}
=> [1,2,4,5,6,3] => [1,2,4,5,6,3] => ? = 4
[1,2,6,3,5,4] => {{1},{2},{3,4,6},{5}}
=> [1,2,4,6,5,3] => [1,2,4,6,5,3] => ? = 3
[1,2,6,4,3,5] => {{1},{2},{3,5,6},{4}}
=> [1,2,5,4,6,3] => [1,2,5,4,6,3] => ? = 3
[1,2,6,4,5,3] => {{1},{2},{3,6},{4},{5}}
=> [1,2,6,4,5,3] => [1,2,6,4,5,3] => ? = 2
[1,2,6,5,3,4] => {{1},{2},{3,4,5,6}}
=> [1,2,4,5,6,3] => [1,2,4,5,6,3] => ? = 4
[1,2,6,5,4,3] => {{1},{2},{3,6},{4,5}}
=> [1,2,6,5,4,3] => [1,2,6,5,4,3] => ? = 2
[1,3,2,4,5,6] => {{1},{2,3},{4},{5},{6}}
=> [1,3,2,4,5,6] => [1,3,2,4,5,6] => ? = 2
[1,3,2,4,6,5] => {{1},{2,3},{4},{5,6}}
=> [1,3,2,4,6,5] => [1,3,2,4,6,5] => ? = 2
[1,3,2,5,4,6] => {{1},{2,3},{4,5},{6}}
=> [1,3,2,5,4,6] => [1,3,2,5,4,6] => ? = 2
[1,3,2,5,6,4] => {{1},{2,3},{4,5,6}}
=> [1,3,2,5,6,4] => [1,3,2,5,6,4] => ? = 6
[1,3,2,6,4,5] => {{1},{2,3},{4,5,6}}
=> [1,3,2,5,6,4] => [1,3,2,5,6,4] => ? = 6
[1,3,2,6,5,4] => {{1},{2,3},{4,6},{5}}
=> [1,3,2,6,5,4] => [1,3,2,6,5,4] => ? = 2
[1,3,4,2,5,6] => {{1},{2,3,4},{5},{6}}
=> [1,3,4,2,5,6] => [1,3,4,2,5,6] => ? = 3
[1,3,4,2,6,5] => {{1},{2,3,4},{5,6}}
=> [1,3,4,2,6,5] => [1,3,4,2,6,5] => ? = 6
[1,3,4,5,2,6] => {{1},{2,3,4,5},{6}}
=> [1,3,4,5,2,6] => [1,3,4,5,2,6] => ? = 4
[1,3,4,5,6,2] => {{1},{2,3,4,5,6}}
=> [1,3,4,5,6,2] => [1,3,4,5,6,2] => ? = 5
[1,3,4,6,2,5] => {{1},{2,3,4,5,6}}
=> [1,3,4,5,6,2] => [1,3,4,5,6,2] => ? = 5
[1,3,4,6,5,2] => {{1},{2,3,4,6},{5}}
=> [1,3,4,6,5,2] => [1,3,4,6,5,2] => ? = 4
[1,3,5,2,4,6] => {{1},{2,3,4,5},{6}}
=> [1,3,4,5,2,6] => [1,3,4,5,2,6] => ? = 4
[1,3,5,2,6,4] => {{1},{2,3,4,5,6}}
=> [1,3,4,5,6,2] => [1,3,4,5,6,2] => ? = 5
[1,3,5,4,2,6] => {{1},{2,3,5},{4},{6}}
=> [1,3,5,4,2,6] => [1,3,5,4,2,6] => ? = 3
[1,3,5,4,6,2] => {{1},{2,3,5,6},{4}}
=> [1,3,5,4,6,2] => [1,3,5,4,6,2] => ? = 4
[1,3,5,6,2,4] => {{1},{2,3,5},{4,6}}
=> [1,3,5,6,2,4] => [1,3,5,6,2,4] => ? = 6
[1,3,5,6,4,2] => {{1},{2,3,4,5,6}}
=> [1,3,4,5,6,2] => [1,3,4,5,6,2] => ? = 5
[1,3,6,2,4,5] => {{1},{2,3,4,5,6}}
=> [1,3,4,5,6,2] => [1,3,4,5,6,2] => ? = 5
[1,3,6,2,5,4] => {{1},{2,3,4,6},{5}}
=> [1,3,4,6,5,2] => [1,3,4,6,5,2] => ? = 4
[1,3,6,4,2,5] => {{1},{2,3,5,6},{4}}
=> [1,3,5,4,6,2] => [1,3,5,4,6,2] => ? = 4
[1,3,6,4,5,2] => {{1},{2,3,6},{4},{5}}
=> [1,3,6,4,5,2] => [1,3,6,4,5,2] => ? = 3
Description
The order of a signed permutation.
Matching statistic: St001207
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 0% ●values known / values provided: 0%●distinct values known / distinct values provided: 17%
Mp00254: Permutations —Inverse fireworks map⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 0% ●values known / values provided: 0%●distinct values known / distinct values provided: 17%
Values
[1,2] => [1,2] => [1,2] => 0 = 1 - 1
[2,1] => [2,1] => [2,1] => 1 = 2 - 1
[1,2,3] => [1,2,3] => [1,2,3] => 0 = 1 - 1
[1,3,2] => [1,3,2] => [1,3,2] => 1 = 2 - 1
[2,1,3] => [2,1,3] => [2,1,3] => 1 = 2 - 1
[2,3,1] => [3,1,2] => [3,1,2] => 2 = 3 - 1
[3,1,2] => [3,2,1] => [3,2,1] => 2 = 3 - 1
[3,2,1] => [2,3,1] => [1,3,2] => 1 = 2 - 1
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0 = 1 - 1
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 1 = 2 - 1
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1 = 2 - 1
[1,3,4,2] => [1,4,2,3] => [1,4,2,3] => 2 = 3 - 1
[1,4,2,3] => [1,4,3,2] => [1,4,3,2] => 2 = 3 - 1
[1,4,3,2] => [1,3,4,2] => [1,2,4,3] => 1 = 2 - 1
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1 = 2 - 1
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 1 = 2 - 1
[2,3,1,4] => [3,1,2,4] => [3,1,2,4] => 2 = 3 - 1
[2,3,4,1] => [4,1,2,3] => [4,1,2,3] => 3 = 4 - 1
[2,4,1,3] => [4,3,1,2] => [4,3,1,2] => 3 = 4 - 1
[2,4,3,1] => [3,4,1,2] => [2,4,1,3] => 2 = 3 - 1
[3,1,2,4] => [3,2,1,4] => [3,2,1,4] => 2 = 3 - 1
[3,1,4,2] => [4,2,1,3] => [4,2,1,3] => 3 = 4 - 1
[3,2,1,4] => [2,3,1,4] => [1,3,2,4] => 1 = 2 - 1
[3,2,4,1] => [2,4,1,3] => [2,4,1,3] => 2 = 3 - 1
[3,4,1,2] => [3,1,4,2] => [2,1,4,3] => 1 = 2 - 1
[3,4,2,1] => [4,1,3,2] => [4,1,3,2] => 3 = 4 - 1
[4,1,2,3] => [4,3,2,1] => [4,3,2,1] => 3 = 4 - 1
[4,1,3,2] => [3,4,2,1] => [1,4,3,2] => 2 = 3 - 1
[4,2,1,3] => [2,4,3,1] => [1,4,3,2] => 2 = 3 - 1
[4,2,3,1] => [2,3,4,1] => [1,2,4,3] => 1 = 2 - 1
[4,3,1,2] => [4,2,3,1] => [4,1,3,2] => 3 = 4 - 1
[4,3,2,1] => [3,2,4,1] => [2,1,4,3] => 1 = 2 - 1
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 1 - 1
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 2 - 1
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => ? = 2 - 1
[1,2,4,5,3] => [1,2,5,3,4] => [1,2,5,3,4] => ? = 3 - 1
[1,2,5,3,4] => [1,2,5,4,3] => [1,2,5,4,3] => ? = 3 - 1
[1,2,5,4,3] => [1,2,4,5,3] => [1,2,3,5,4] => ? = 2 - 1
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => ? = 2 - 1
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ? = 2 - 1
[1,3,4,2,5] => [1,4,2,3,5] => [1,4,2,3,5] => ? = 3 - 1
[1,3,4,5,2] => [1,5,2,3,4] => [1,5,2,3,4] => ? = 4 - 1
[1,3,5,2,4] => [1,5,4,2,3] => [1,5,4,2,3] => ? = 4 - 1
[1,3,5,4,2] => [1,4,5,2,3] => [1,3,5,2,4] => ? = 3 - 1
[1,4,2,3,5] => [1,4,3,2,5] => [1,4,3,2,5] => ? = 3 - 1
[1,4,2,5,3] => [1,5,3,2,4] => [1,5,3,2,4] => ? = 4 - 1
[1,4,3,2,5] => [1,3,4,2,5] => [1,2,4,3,5] => ? = 2 - 1
[1,4,3,5,2] => [1,3,5,2,4] => [1,3,5,2,4] => ? = 3 - 1
[1,4,5,2,3] => [1,4,2,5,3] => [1,3,2,5,4] => ? = 2 - 1
[1,4,5,3,2] => [1,5,2,4,3] => [1,5,2,4,3] => ? = 4 - 1
[1,5,2,3,4] => [1,5,4,3,2] => [1,5,4,3,2] => ? = 4 - 1
[1,5,2,4,3] => [1,4,5,3,2] => [1,2,5,4,3] => ? = 3 - 1
[1,5,3,2,4] => [1,3,5,4,2] => [1,2,5,4,3] => ? = 3 - 1
[1,5,3,4,2] => [1,3,4,5,2] => [1,2,3,5,4] => ? = 2 - 1
[1,5,4,2,3] => [1,5,3,4,2] => [1,5,2,4,3] => ? = 4 - 1
[1,5,4,3,2] => [1,4,3,5,2] => [1,3,2,5,4] => ? = 2 - 1
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ? = 2 - 1
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 2 - 1
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 2 - 1
[2,1,4,5,3] => [2,1,5,3,4] => [2,1,5,3,4] => ? = 6 - 1
[2,1,5,3,4] => [2,1,5,4,3] => [2,1,5,4,3] => ? = 6 - 1
[2,1,5,4,3] => [2,1,4,5,3] => [2,1,3,5,4] => ? = 2 - 1
[2,3,1,4,5] => [3,1,2,4,5] => [3,1,2,4,5] => ? = 3 - 1
[2,3,1,5,4] => [3,1,2,5,4] => [3,1,2,5,4] => ? = 6 - 1
[2,3,4,1,5] => [4,1,2,3,5] => [4,1,2,3,5] => ? = 4 - 1
[2,3,4,5,1] => [5,1,2,3,4] => [5,1,2,3,4] => ? = 5 - 1
[2,3,5,1,4] => [5,4,1,2,3] => [5,4,1,2,3] => ? = 5 - 1
[2,3,5,4,1] => [4,5,1,2,3] => [3,5,1,2,4] => ? = 4 - 1
[2,4,1,3,5] => [4,3,1,2,5] => [4,3,1,2,5] => ? = 4 - 1
[2,4,1,5,3] => [5,3,1,2,4] => [5,3,1,2,4] => ? = 5 - 1
[2,4,3,1,5] => [3,4,1,2,5] => [2,4,1,3,5] => ? = 3 - 1
[2,4,3,5,1] => [3,5,1,2,4] => [3,5,1,2,4] => ? = 4 - 1
[2,4,5,1,3] => [4,1,2,5,3] => [3,1,2,5,4] => ? = 6 - 1
[2,4,5,3,1] => [5,1,2,4,3] => [5,1,2,4,3] => ? = 5 - 1
[2,5,1,3,4] => [5,4,3,1,2] => [5,4,3,1,2] => ? = 5 - 1
[2,5,1,4,3] => [4,5,3,1,2] => [2,5,4,1,3] => ? = 4 - 1
[2,5,3,1,4] => [3,5,4,1,2] => [2,5,4,1,3] => ? = 4 - 1
[2,5,3,4,1] => [3,4,5,1,2] => [1,3,5,2,4] => ? = 3 - 1
[2,5,4,1,3] => [5,3,4,1,2] => [5,2,4,1,3] => ? = 5 - 1
[2,5,4,3,1] => [4,3,5,1,2] => [3,2,5,1,4] => ? = 6 - 1
[3,1,2,4,5] => [3,2,1,4,5] => [3,2,1,4,5] => ? = 3 - 1
[3,1,2,5,4] => [3,2,1,5,4] => [3,2,1,5,4] => ? = 6 - 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]/(xn).
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