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Your data matches 9 different statistics following compositions of up to 3 maps.
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Matching statistic: St000018
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(load all 2 compositions to match this statistic)
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
St000018: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00067: Permutations —Foata bijection⟶ Permutations
St000018: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
=> [1] => [1] => [1] => 0
{{1,2}}
=> [2,1] => [1,2] => [1,2] => 0
{{1},{2}}
=> [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
=> [2,3,1] => [1,2,3] => [1,2,3] => 0
{{1,2},{3}}
=> [2,1,3] => [1,2,3] => [1,2,3] => 0
{{1,3},{2}}
=> [3,2,1] => [1,3,2] => [3,1,2] => 2
{{1},{2,3}}
=> [1,3,2] => [1,2,3] => [1,2,3] => 0
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
=> [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3},{4}}
=> [2,3,1,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,4},{3}}
=> [2,4,3,1] => [1,2,4,3] => [4,1,2,3] => 3
{{1,2},{3,4}}
=> [2,1,4,3] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,3,4},{2}}
=> [3,2,4,1] => [1,3,4,2] => [3,1,4,2] => 3
{{1,3},{2,4}}
=> [3,4,1,2] => [1,3,2,4] => [3,1,2,4] => 2
{{1,3},{2},{4}}
=> [3,2,1,4] => [1,3,2,4] => [3,1,2,4] => 2
{{1,4},{2,3}}
=> [4,3,2,1] => [1,4,2,3] => [1,4,2,3] => 2
{{1},{2,3,4}}
=> [1,3,4,2] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,4},{2},{3}}
=> [4,2,3,1] => [1,4,2,3] => [1,4,2,3] => 2
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,2,4,3] => [4,1,2,3] => 3
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,3,4] => [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}}
=> [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,2,3,5,4] => [5,1,2,3,4] => 4
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,2,4,5,3] => [4,1,2,5,3] => 4
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,2,4,3,5] => [4,1,2,3,5] => 3
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,2,4,3,5] => [4,1,2,3,5] => 3
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,2,5,3,4] => [1,5,2,3,4] => 3
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,2,5,3,4] => [1,5,2,3,4] => 3
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,2,3,5,4] => [5,1,2,3,4] => 4
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [1,3,4,5,2] => [3,1,4,5,2] => 4
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [1,3,4,2,5] => [3,1,4,2,5] => 3
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,3,4,2,5] => [3,1,4,2,5] => 3
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [1,3,5,2,4] => [3,1,2,5,4] => 3
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [1,3,2,4,5] => [3,1,2,4,5] => 2
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [1,3,2,4,5] => [3,1,2,4,5] => 2
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [1,3,5,2,4] => [3,1,2,5,4] => 3
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [1,3,2,5,4] => [5,3,1,2,4] => 6
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [1,3,2,4,5] => [3,1,2,4,5] => 2
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,3,2,4,5] => [3,1,2,4,5] => 2
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [1,4,5,2,3] => [1,4,2,5,3] => 3
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [1,4,2,3,5] => [1,4,2,3,5] => 2
Description
The number of inversions of a permutation.
This equals the minimal number of simple transpositions $(i,i+1)$ needed to write $\pi$. Thus, it is also the Coxeter length of $\pi$.
Matching statistic: St000391
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
St000391: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00109: Permutations —descent word⟶ Binary words
St000391: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
=> [1] => [1] => => ? = 0
{{1,2}}
=> [2,1] => [1,2] => 0 => 0
{{1},{2}}
=> [1,2] => [1,2] => 0 => 0
{{1,2,3}}
=> [2,3,1] => [1,2,3] => 00 => 0
{{1,2},{3}}
=> [2,1,3] => [1,2,3] => 00 => 0
{{1,3},{2}}
=> [3,2,1] => [1,3,2] => 01 => 2
{{1},{2,3}}
=> [1,3,2] => [1,2,3] => 00 => 0
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => 00 => 0
{{1,2,3,4}}
=> [2,3,4,1] => [1,2,3,4] => 000 => 0
{{1,2,3},{4}}
=> [2,3,1,4] => [1,2,3,4] => 000 => 0
{{1,2,4},{3}}
=> [2,4,3,1] => [1,2,4,3] => 001 => 3
{{1,2},{3,4}}
=> [2,1,4,3] => [1,2,3,4] => 000 => 0
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,2,3,4] => 000 => 0
{{1,3,4},{2}}
=> [3,2,4,1] => [1,3,4,2] => 001 => 3
{{1,3},{2,4}}
=> [3,4,1,2] => [1,3,2,4] => 010 => 2
{{1,3},{2},{4}}
=> [3,2,1,4] => [1,3,2,4] => 010 => 2
{{1,4},{2,3}}
=> [4,3,2,1] => [1,4,2,3] => 010 => 2
{{1},{2,3,4}}
=> [1,3,4,2] => [1,2,3,4] => 000 => 0
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,2,3,4] => 000 => 0
{{1,4},{2},{3}}
=> [4,2,3,1] => [1,4,2,3] => 010 => 2
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,2,4,3] => 001 => 3
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,3,4] => 000 => 0
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => 000 => 0
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [1,2,3,4,5] => 0000 => 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,2,3,4,5] => 0000 => 0
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,2,3,5,4] => 0001 => 4
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,2,3,4,5] => 0000 => 0
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,2,3,4,5] => 0000 => 0
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,2,4,5,3] => 0001 => 4
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,2,4,3,5] => 0010 => 3
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,2,4,3,5] => 0010 => 3
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,2,5,3,4] => 0010 => 3
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,2,3,4,5] => 0000 => 0
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,2,3,4,5] => 0000 => 0
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,2,5,3,4] => 0010 => 3
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,2,3,5,4] => 0001 => 4
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,2,3,4,5] => 0000 => 0
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [1,2,3,4,5] => 0000 => 0
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [1,3,4,5,2] => 0001 => 4
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [1,3,4,2,5] => 0010 => 3
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,3,4,2,5] => 0010 => 3
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [1,3,5,2,4] => 0010 => 3
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [1,3,2,4,5] => 0100 => 2
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [1,3,2,4,5] => 0100 => 2
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [1,3,5,2,4] => 0010 => 3
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [1,3,2,5,4] => 0101 => 6
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [1,3,2,4,5] => 0100 => 2
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,3,2,4,5] => 0100 => 2
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [1,4,5,2,3] => 0010 => 3
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [1,4,2,3,5] => 0100 => 2
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [1,4,2,3,5] => 0100 => 2
Description
The sum of the positions of the ones in a binary word.
Matching statistic: St000330
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
St000330: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
St000330: Standard tableaux ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
=> [1] => [1] => [[1]]
=> 0
{{1,2}}
=> [2,1] => [1,2] => [[1,2]]
=> 0
{{1},{2}}
=> [1,2] => [1,2] => [[1,2]]
=> 0
{{1,2,3}}
=> [2,3,1] => [1,2,3] => [[1,2,3]]
=> 0
{{1,2},{3}}
=> [2,1,3] => [1,2,3] => [[1,2,3]]
=> 0
{{1,3},{2}}
=> [3,2,1] => [1,3,2] => [[1,2],[3]]
=> 2
{{1},{2,3}}
=> [1,3,2] => [1,2,3] => [[1,2,3]]
=> 0
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => [[1,2,3]]
=> 0
{{1,2,3,4}}
=> [2,3,4,1] => [1,2,3,4] => [[1,2,3,4]]
=> 0
{{1,2,3},{4}}
=> [2,3,1,4] => [1,2,3,4] => [[1,2,3,4]]
=> 0
{{1,2,4},{3}}
=> [2,4,3,1] => [1,2,4,3] => [[1,2,3],[4]]
=> 3
{{1,2},{3,4}}
=> [2,1,4,3] => [1,2,3,4] => [[1,2,3,4]]
=> 0
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,2,3,4] => [[1,2,3,4]]
=> 0
{{1,3,4},{2}}
=> [3,2,4,1] => [1,3,4,2] => [[1,2,3],[4]]
=> 3
{{1,3},{2,4}}
=> [3,4,1,2] => [1,3,2,4] => [[1,2,4],[3]]
=> 2
{{1,3},{2},{4}}
=> [3,2,1,4] => [1,3,2,4] => [[1,2,4],[3]]
=> 2
{{1,4},{2,3}}
=> [4,3,2,1] => [1,4,2,3] => [[1,2,4],[3]]
=> 2
{{1},{2,3,4}}
=> [1,3,4,2] => [1,2,3,4] => [[1,2,3,4]]
=> 0
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,2,3,4] => [[1,2,3,4]]
=> 0
{{1,4},{2},{3}}
=> [4,2,3,1] => [1,4,2,3] => [[1,2,4],[3]]
=> 2
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,2,4,3] => [[1,2,3],[4]]
=> 3
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,3,4] => [[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}}
=> [2,3,4,5,1] => [1,2,3,4,5] => [[1,2,3,4,5]]
=> 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,2,3,4,5] => [[1,2,3,4,5]]
=> 0
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,2,3,5,4] => [[1,2,3,4],[5]]
=> 4
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,2,3,4,5] => [[1,2,3,4,5]]
=> 0
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,2,3,4,5] => [[1,2,3,4,5]]
=> 0
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,2,4,5,3] => [[1,2,3,4],[5]]
=> 4
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,2,4,3,5] => [[1,2,3,5],[4]]
=> 3
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,2,4,3,5] => [[1,2,3,5],[4]]
=> 3
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,2,5,3,4] => [[1,2,3,5],[4]]
=> 3
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,2,3,4,5] => [[1,2,3,4,5]]
=> 0
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,2,3,4,5] => [[1,2,3,4,5]]
=> 0
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,2,5,3,4] => [[1,2,3,5],[4]]
=> 3
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,2,3,5,4] => [[1,2,3,4],[5]]
=> 4
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,2,3,4,5] => [[1,2,3,4,5]]
=> 0
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [1,2,3,4,5] => [[1,2,3,4,5]]
=> 0
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [1,3,4,5,2] => [[1,2,3,4],[5]]
=> 4
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [1,3,4,2,5] => [[1,2,3,5],[4]]
=> 3
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,3,4,2,5] => [[1,2,3,5],[4]]
=> 3
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [1,3,5,2,4] => [[1,2,3],[4,5]]
=> 3
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [1,3,2,4,5] => [[1,2,4,5],[3]]
=> 2
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [1,3,2,4,5] => [[1,2,4,5],[3]]
=> 2
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [1,3,5,2,4] => [[1,2,3],[4,5]]
=> 3
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [1,3,2,5,4] => [[1,2,4],[3,5]]
=> 6
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [1,3,2,4,5] => [[1,2,4,5],[3]]
=> 2
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,3,2,4,5] => [[1,2,4,5],[3]]
=> 2
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [1,4,5,2,3] => [[1,2,3],[4,5]]
=> 3
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [1,4,2,3,5] => [[1,2,4,5],[3]]
=> 2
{{1},{2},{3},{4},{5},{6,9},{7},{8}}
=> [1,2,3,4,5,9,7,8,6] => [1,2,3,4,5,6,9,7,8] => [[1,2,3,4,5,6,7,9],[8]]
=> ? = 7
{{1,2,3,4,5,6,8},{7},{9}}
=> [2,3,4,5,6,8,7,1,9] => [1,2,3,4,5,6,8,7,9] => [[1,2,3,4,5,6,7,9],[8]]
=> ? = 7
{{1},{2},{3},{4},{5},{6,8},{7,9}}
=> [1,2,3,4,5,8,9,6,7] => [1,2,3,4,5,6,8,7,9] => [[1,2,3,4,5,6,7,9],[8]]
=> ? = 7
{{1},{2,3,4,5,6,8},{7,9}}
=> [1,3,4,5,6,8,9,2,7] => [1,2,3,4,5,6,8,7,9] => [[1,2,3,4,5,6,7,9],[8]]
=> ? = 7
Description
The (standard) major index of a standard tableau.
A descent of a standard tableau $T$ is an index $i$ such that $i+1$ appears in a row strictly below the row of $i$. The (standard) major index is the the sum of the descents.
Matching statistic: St000008
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
St000008: Integer compositions ⟶ ℤResult quality: 95% ●values known / values provided: 95%●distinct values known / distinct values provided: 100%
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
St000008: Integer compositions ⟶ ℤResult quality: 95% ●values known / values provided: 95%●distinct values known / distinct values provided: 100%
Values
{{1}}
=> [1] => [1] => [1] => 0
{{1,2}}
=> [2,1] => [1,2] => [2] => 0
{{1},{2}}
=> [1,2] => [1,2] => [2] => 0
{{1,2,3}}
=> [2,3,1] => [1,2,3] => [3] => 0
{{1,2},{3}}
=> [2,1,3] => [1,2,3] => [3] => 0
{{1,3},{2}}
=> [3,2,1] => [1,3,2] => [2,1] => 2
{{1},{2,3}}
=> [1,3,2] => [1,2,3] => [3] => 0
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => [3] => 0
{{1,2,3,4}}
=> [2,3,4,1] => [1,2,3,4] => [4] => 0
{{1,2,3},{4}}
=> [2,3,1,4] => [1,2,3,4] => [4] => 0
{{1,2,4},{3}}
=> [2,4,3,1] => [1,2,4,3] => [3,1] => 3
{{1,2},{3,4}}
=> [2,1,4,3] => [1,2,3,4] => [4] => 0
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,2,3,4] => [4] => 0
{{1,3,4},{2}}
=> [3,2,4,1] => [1,3,4,2] => [3,1] => 3
{{1,3},{2,4}}
=> [3,4,1,2] => [1,3,2,4] => [2,2] => 2
{{1,3},{2},{4}}
=> [3,2,1,4] => [1,3,2,4] => [2,2] => 2
{{1,4},{2,3}}
=> [4,3,2,1] => [1,4,2,3] => [2,2] => 2
{{1},{2,3,4}}
=> [1,3,4,2] => [1,2,3,4] => [4] => 0
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,2,3,4] => [4] => 0
{{1,4},{2},{3}}
=> [4,2,3,1] => [1,4,2,3] => [2,2] => 2
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,2,4,3] => [3,1] => 3
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,3,4] => [4] => 0
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => [4] => 0
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [1,2,3,4,5] => [5] => 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,2,3,4,5] => [5] => 0
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,2,3,5,4] => [4,1] => 4
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,2,3,4,5] => [5] => 0
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,2,3,4,5] => [5] => 0
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,2,4,5,3] => [4,1] => 4
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,2,4,3,5] => [3,2] => 3
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,2,4,3,5] => [3,2] => 3
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,2,5,3,4] => [3,2] => 3
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,2,3,4,5] => [5] => 0
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,2,3,4,5] => [5] => 0
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,2,5,3,4] => [3,2] => 3
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,2,3,5,4] => [4,1] => 4
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,2,3,4,5] => [5] => 0
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [1,2,3,4,5] => [5] => 0
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [1,3,4,5,2] => [4,1] => 4
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [1,3,4,2,5] => [3,2] => 3
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,3,4,2,5] => [3,2] => 3
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [1,3,5,2,4] => [3,2] => 3
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [1,3,2,4,5] => [2,3] => 2
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [1,3,2,4,5] => [2,3] => 2
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [1,3,5,2,4] => [3,2] => 3
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [1,3,2,5,4] => [2,2,1] => 6
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [1,3,2,4,5] => [2,3] => 2
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,3,2,4,5] => [2,3] => 2
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [1,4,5,2,3] => [3,2] => 3
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [1,4,2,3,5] => [2,3] => 2
{{1,2},{3,4},{5,6},{7,8},{9,10}}
=> [2,1,4,3,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
=> [1,2,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1},{2},{3},{4},{5},{6},{7},{8,9}}
=> [1,2,3,4,5,6,7,9,8] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1},{2},{3},{4},{5},{6,9},{7},{8}}
=> [1,2,3,4,5,9,7,8,6] => [1,2,3,4,5,6,9,7,8] => [7,2] => ? = 7
{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
=> [1,2,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
=> [1,2,3,4,5,6,7,8,10,9] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1},{2},{3},{4},{5},{6},{7,8,9}}
=> [1,2,3,4,5,6,8,9,7] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1},{2},{3},{4},{5},{6},{7,10},{8},{9}}
=> [1,2,3,4,5,6,10,8,9,7] => [1,2,3,4,5,6,7,10,8,9] => [8,2] => ? = 8
{{1,2,3,4,5,6,7,8},{9}}
=> [2,3,4,5,6,7,8,1,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1},{2,3,4,5,6,7,8,9}}
=> [1,3,4,5,6,7,8,9,2] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4,5,6,7,8,9},{10}}
=> [2,3,4,5,6,7,8,9,1,10] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4,5,6,8},{7},{9}}
=> [2,3,4,5,6,8,7,1,9] => [1,2,3,4,5,6,8,7,9] => [7,2] => ? = 7
{{1},{2,3,4,5,6,7,8,9,10}}
=> [1,3,4,5,6,7,8,9,10,2] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4,5,6,7,9},{8},{10}}
=> [2,3,4,5,6,7,9,8,1,10] => [1,2,3,4,5,6,7,9,8,10] => [8,2] => ? = 8
{{1,2,3,4,5},{6,7,8,9,10}}
=> [2,3,4,5,1,7,8,9,10,6] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2},{3},{4},{5},{6},{7},{8},{9}}
=> [2,1,3,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}
=> [2,1,3,4,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3},{4},{5},{6},{7},{8},{9}}
=> [2,3,1,4,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4,5,6,7,8,9}}
=> [2,3,4,5,6,7,8,9,1] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4,5,6,7},{8,9}}
=> [2,3,4,5,6,7,1,9,8] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4,5,6,7},{8},{9}}
=> [2,3,4,5,6,7,1,8,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4,5,6},{7,8,9}}
=> [2,3,4,5,6,1,8,9,7] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4,5,6},{7,8},{9}}
=> [2,3,4,5,6,1,8,7,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4,5,6},{7},{8},{9}}
=> [2,3,4,5,6,1,7,8,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4,5},{6,7,8,9}}
=> [2,3,4,5,1,7,8,9,6] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4,5},{6,7},{8,9}}
=> [2,3,4,5,1,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4,5},{6,7},{8},{9}}
=> [2,3,4,5,1,7,6,8,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4,5},{6},{7},{8},{9}}
=> [2,3,4,5,1,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4},{5,6},{7,8},{9}}
=> [2,3,4,1,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4},{5,6},{7},{8},{9}}
=> [2,3,4,1,6,5,7,8,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4},{5},{6},{7},{8},{9}}
=> [2,3,4,1,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3},{4,5},{6,7},{8,9}}
=> [2,3,1,5,4,7,6,9,8] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3},{4,5},{6},{7},{8},{9}}
=> [2,3,1,5,4,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2},{3,4},{5,6},{7,8},{9}}
=> [2,1,4,3,6,5,8,7,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2},{3,4},{5,6},{7},{8},{9}}
=> [2,1,4,3,6,5,7,8,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2},{3,4},{5},{6},{7},{8},{9}}
=> [2,1,4,3,5,6,7,8,9] => [1,2,3,4,5,6,7,8,9] => [9] => ? = 0
{{1,2,3,4,5,6,7,8,9,10}}
=> [2,3,4,5,6,7,8,9,10,1] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4,5,6,7,8},{9,10}}
=> [2,3,4,5,6,7,8,1,10,9] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4,5,6,7,8},{9},{10}}
=> [2,3,4,5,6,7,8,1,9,10] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4,5,6,7},{8,9,10}}
=> [2,3,4,5,6,7,1,9,10,8] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4,5,6,7},{8,9},{10}}
=> [2,3,4,5,6,7,1,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4,5,6,7},{8},{9},{10}}
=> [2,3,4,5,6,7,1,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4,5,6},{7,8,9,10}}
=> [2,3,4,5,6,1,8,9,10,7] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4,5,6},{7,8},{9,10}}
=> [2,3,4,5,6,1,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4,5,6},{7},{8},{9},{10}}
=> [2,3,4,5,6,1,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4,5},{6,7},{8,9},{10}}
=> [2,3,4,5,1,7,6,9,8,10] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4,5},{6},{7},{8},{9},{10}}
=> [2,3,4,5,1,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4},{5,6,7,8},{9,10}}
=> [2,3,4,1,6,7,8,5,10,9] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4},{5,6},{7,8},{9,10}}
=> [2,3,4,1,6,5,8,7,10,9] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
{{1,2,3,4},{5},{6},{7},{8},{9},{10}}
=> [2,3,4,1,5,6,7,8,9,10] => [1,2,3,4,5,6,7,8,9,10] => [10] => ? = 0
Description
The major index of the composition.
The descents of a composition $[c_1,c_2,\dots,c_k]$ are the partial sums $c_1, c_1+c_2,\dots, c_1+\dots+c_{k-1}$, excluding the sum of all parts. The major index of a composition is the sum of its descents.
For details about the major index see [[Permutations/Descents-Major]].
Matching statistic: St000748
St000748: Set partitions ⟶ ℤResult quality: 56% ●values known / values provided: 56%●distinct values known / distinct values provided: 79%
Values
{{1}}
=> ? = 0
{{1,2}}
=> 0
{{1},{2}}
=> 0
{{1,2,3}}
=> 0
{{1,2},{3}}
=> 0
{{1,3},{2}}
=> 2
{{1},{2,3}}
=> 0
{{1},{2},{3}}
=> 0
{{1,2,3,4}}
=> 0
{{1,2,3},{4}}
=> 0
{{1,2,4},{3}}
=> 3
{{1,2},{3,4}}
=> 0
{{1,2},{3},{4}}
=> 0
{{1,3,4},{2}}
=> 3
{{1,3},{2,4}}
=> 2
{{1,3},{2},{4}}
=> 2
{{1,4},{2,3}}
=> 2
{{1},{2,3,4}}
=> 0
{{1},{2,3},{4}}
=> 0
{{1,4},{2},{3}}
=> 2
{{1},{2,4},{3}}
=> 3
{{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}}
=> 4
{{1,2,3},{4,5}}
=> 0
{{1,2,3},{4},{5}}
=> 0
{{1,2,4,5},{3}}
=> 4
{{1,2,4},{3,5}}
=> 3
{{1,2,4},{3},{5}}
=> 3
{{1,2,5},{3,4}}
=> 3
{{1,2},{3,4,5}}
=> 0
{{1,2},{3,4},{5}}
=> 0
{{1,2,5},{3},{4}}
=> 3
{{1,2},{3,5},{4}}
=> 4
{{1,2},{3},{4,5}}
=> 0
{{1,2},{3},{4},{5}}
=> 0
{{1,3,4,5},{2}}
=> 4
{{1,3,4},{2,5}}
=> 3
{{1,3,4},{2},{5}}
=> 3
{{1,3,5},{2,4}}
=> 3
{{1,3},{2,4,5}}
=> 2
{{1,3},{2,4},{5}}
=> 2
{{1,3,5},{2},{4}}
=> 3
{{1,3},{2,5},{4}}
=> 6
{{1,3},{2},{4,5}}
=> 2
{{1,3},{2},{4},{5}}
=> 2
{{1,4,5},{2,3}}
=> 3
{{1,4},{2,3,5}}
=> 2
{{1,4},{2,3},{5}}
=> 2
{{1,2},{3,4},{5,6},{7,8}}
=> ? = 0
{{1,4},{2,3},{5,6},{7,8}}
=> ? = 2
{{1,6},{2,3},{4,5},{7,8}}
=> ? = 2
{{1,8},{2,3},{4,5},{6,7}}
=> ? = 2
{{1,8},{2,4},{3,5},{6,7}}
=> ? = 6
{{1,2},{3,5},{4,6},{7,8}}
=> ? = 4
{{1,2},{3,6},{4,5},{7,8}}
=> ? = 4
{{1,6},{2,5},{3,4},{7,8}}
=> ? = 6
{{1,5},{2,7},{3,4},{6,8}}
=> ? = 6
{{1,2},{3,8},{4,5},{6,7}}
=> ? = 4
{{1,4},{2,8},{3,5},{6,7}}
=> ? = 6
{{1,8},{2,7},{3,4},{5,6}}
=> ? = 6
{{1,5},{2,6},{3,7},{4,8}}
=> ? = 12
{{1,2},{3,6},{4,7},{5,8}}
=> ? = 10
{{1,6},{2,3},{4,7},{5,8}}
=> ? = 8
{{1,2},{3,4},{5,7},{6,8}}
=> ? = 6
{{1,2},{3,4},{5,8},{6,7}}
=> ? = 6
{{1,5},{2,3},{4,8},{6,7}}
=> ? = 8
{{1,7},{2,3},{4,8},{5,6}}
=> ? = 8
{{1,8},{2,3},{4,7},{5,6}}
=> ? = 8
{{1,2},{3,6},{4,8},{5,7}}
=> ? = 10
{{1,6},{2,7},{3,8},{4,5}}
=> ? = 12
{{1,2},{3,7},{4,8},{5,6}}
=> ? = 10
{{1,2},{3,8},{4,7},{5,6}}
=> ? = 10
{{1,8},{2,7},{3,6},{4,5}}
=> ? = 12
{{1,2},{3,4},{5,6},{7,8},{9,10}}
=> ? = 0
{{1},{2},{3},{4},{5},{6},{7},{8}}
=> ? = 0
{{1},{2},{3},{4},{5},{6},{7,8}}
=> ? = 0
{{1},{2},{3},{4},{5},{6,8},{7}}
=> ? = 7
{{1},{2},{3},{4},{5},{6,7,8}}
=> ? = 0
{{1},{2},{3},{4},{5,8},{6},{7}}
=> ? = 6
{{1},{2},{3},{4},{5,7,8},{6}}
=> ? = 7
{{1},{2},{3},{4},{5,8},{6,7}}
=> ? = 6
{{1},{2},{3},{4},{5,6,8},{7}}
=> ? = 7
{{1},{2},{3},{4},{5,6,7,8}}
=> ? = 0
{{1},{2},{3},{4,6,8},{5},{7}}
=> ? = 6
{{1},{2},{3},{4,7,8},{5,6}}
=> ? = 6
{{1},{2},{3},{4,5,8},{6},{7}}
=> ? = 6
{{1},{2},{3},{4,5,6,8},{7}}
=> ? = 7
{{1},{2},{3},{4,5,6,7,8}}
=> ? = 0
{{1},{2},{3,4},{5,6},{7},{8}}
=> ? = 0
{{1},{2},{3,4},{5,8},{6,7}}
=> ? = 6
{{1},{2},{3,4},{5,6,7,8}}
=> ? = 0
{{1},{2},{3,5},{4},{6,7,8}}
=> ? = 4
{{1},{2},{3,8},{4},{5},{6},{7}}
=> ? = 4
{{1},{2},{3,5,8},{4},{6},{7}}
=> ? = 5
{{1},{2},{3,8},{4},{5,6,7}}
=> ? = 4
{{1},{2},{3,5,8},{4},{6,7}}
=> ? = 5
{{1},{2},{3,4,5},{6,7,8}}
=> ? = 0
Description
The major index of the permutation obtained by flattening the set partition.
A set partition can be represented by a sequence of blocks where the first entries of the blocks and the blocks themselves are increasing. This statistic is then the major index of the permutation obtained by flattening the set partition in this canonical form.
Matching statistic: St000833
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St000833: Permutations ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 57%
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00126: Permutations —cactus evacuation⟶ Permutations
St000833: Permutations ⟶ ℤResult quality: 40% ●values known / values provided: 40%●distinct values known / distinct values provided: 57%
Values
{{1}}
=> [1] => [1] => [1] => ? = 0
{{1,2}}
=> [2,1] => [1,2] => [1,2] => 0
{{1},{2}}
=> [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
=> [2,3,1] => [1,2,3] => [1,2,3] => 0
{{1,2},{3}}
=> [2,1,3] => [1,2,3] => [1,2,3] => 0
{{1,3},{2}}
=> [3,2,1] => [1,3,2] => [3,1,2] => 2
{{1},{2,3}}
=> [1,3,2] => [1,2,3] => [1,2,3] => 0
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
=> [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3},{4}}
=> [2,3,1,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,4},{3}}
=> [2,4,3,1] => [1,2,4,3] => [4,1,2,3] => 3
{{1,2},{3,4}}
=> [2,1,4,3] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,3,4},{2}}
=> [3,2,4,1] => [1,3,4,2] => [3,1,2,4] => 3
{{1,3},{2,4}}
=> [3,4,1,2] => [1,3,2,4] => [1,3,2,4] => 2
{{1,3},{2},{4}}
=> [3,2,1,4] => [1,3,2,4] => [1,3,2,4] => 2
{{1,4},{2,3}}
=> [4,3,2,1] => [1,4,2,3] => [1,4,2,3] => 2
{{1},{2,3,4}}
=> [1,3,4,2] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,4},{2},{3}}
=> [4,2,3,1] => [1,4,2,3] => [1,4,2,3] => 2
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,2,4,3] => [4,1,2,3] => 3
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,3,4] => [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}}
=> [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,2,3,5,4] => [5,1,2,3,4] => 4
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,2,4,5,3] => [4,1,2,3,5] => 4
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,2,4,3,5] => [1,4,2,3,5] => 3
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,2,4,3,5] => [1,4,2,3,5] => 3
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,2,5,3,4] => [1,5,2,3,4] => 3
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,2,5,3,4] => [1,5,2,3,4] => 3
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,2,3,5,4] => [5,1,2,3,4] => 4
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [1,3,4,5,2] => [3,1,2,4,5] => 4
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [1,3,4,2,5] => [1,3,2,4,5] => 3
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,3,4,2,5] => [1,3,2,4,5] => 3
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [1,3,5,2,4] => [3,5,1,2,4] => 3
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [1,3,2,4,5] => [1,3,4,2,5] => 2
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [1,3,2,4,5] => [1,3,4,2,5] => 2
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [1,3,5,2,4] => [3,5,1,2,4] => 3
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [1,3,2,5,4] => [3,1,5,2,4] => 6
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [1,3,2,4,5] => [1,3,4,2,5] => 2
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,3,2,4,5] => [1,3,4,2,5] => 2
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [1,4,5,2,3] => [4,5,1,2,3] => 3
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [1,4,2,3,5] => [1,2,4,3,5] => 2
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [1,4,2,3,5] => [1,2,4,3,5] => 2
{{1,2,3,4,5,7},{6}}
=> [2,3,4,5,7,6,1] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => ? = 6
{{1,2,3,4,6,7},{5}}
=> [2,3,4,6,5,7,1] => [1,2,3,4,6,7,5] => [6,1,2,3,4,5,7] => ? = 6
{{1,2,3,4,6},{5,7}}
=> [2,3,4,6,7,1,5] => [1,2,3,4,6,5,7] => [1,6,2,3,4,5,7] => ? = 5
{{1,2,3,4,6},{5},{7}}
=> [2,3,4,6,5,1,7] => [1,2,3,4,6,5,7] => [1,6,2,3,4,5,7] => ? = 5
{{1,2,3,4,7},{5,6}}
=> [2,3,4,7,6,5,1] => [1,2,3,4,7,5,6] => [1,7,2,3,4,5,6] => ? = 5
{{1,2,3,4,7},{5},{6}}
=> [2,3,4,7,5,6,1] => [1,2,3,4,7,5,6] => [1,7,2,3,4,5,6] => ? = 5
{{1,2,3,4},{5,7},{6}}
=> [2,3,4,1,7,6,5] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => ? = 6
{{1,2,3,5,6,7},{4}}
=> [2,3,5,4,6,7,1] => [1,2,3,5,6,7,4] => [5,1,2,3,4,6,7] => ? = 6
{{1,2,3,5,6},{4,7}}
=> [2,3,5,7,6,1,4] => [1,2,3,5,6,4,7] => [1,5,2,3,4,6,7] => ? = 5
{{1,2,3,5,6},{4},{7}}
=> [2,3,5,4,6,1,7] => [1,2,3,5,6,4,7] => [1,5,2,3,4,6,7] => ? = 5
{{1,2,3,5,7},{4,6}}
=> [2,3,5,6,7,4,1] => [1,2,3,5,7,4,6] => [5,7,1,2,3,4,6] => ? = 5
{{1,2,3,5,7},{4},{6}}
=> [2,3,5,4,7,6,1] => [1,2,3,5,7,4,6] => [5,7,1,2,3,4,6] => ? = 5
{{1,2,3,5},{4,7},{6}}
=> [2,3,5,7,1,6,4] => [1,2,3,5,4,7,6] => [5,1,7,2,3,4,6] => ? = 10
{{1,2,3,6,7},{4,5}}
=> [2,3,6,5,4,7,1] => [1,2,3,6,7,4,5] => [6,7,1,2,3,4,5] => ? = 5
{{1,2,3},{4,5,7},{6}}
=> [2,3,1,5,7,6,4] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => ? = 6
{{1,2,3,6,7},{4},{5}}
=> [2,3,6,4,5,7,1] => [1,2,3,6,7,4,5] => [6,7,1,2,3,4,5] => ? = 5
{{1,2,3,6},{4,7},{5}}
=> [2,3,6,7,5,1,4] => [1,2,3,6,4,7,5] => [6,1,7,2,3,4,5] => ? = 10
{{1,2,3},{4,6,7},{5}}
=> [2,3,1,6,5,7,4] => [1,2,3,4,6,7,5] => [6,1,2,3,4,5,7] => ? = 6
{{1,2,3},{4,6},{5,7}}
=> [2,3,1,6,7,4,5] => [1,2,3,4,6,5,7] => [1,6,2,3,4,5,7] => ? = 5
{{1,2,3},{4,6},{5},{7}}
=> [2,3,1,6,5,4,7] => [1,2,3,4,6,5,7] => [1,6,2,3,4,5,7] => ? = 5
{{1,2,3},{4,7},{5,6}}
=> [2,3,1,7,6,5,4] => [1,2,3,4,7,5,6] => [1,7,2,3,4,5,6] => ? = 5
{{1,2,3},{4,7},{5},{6}}
=> [2,3,1,7,5,6,4] => [1,2,3,4,7,5,6] => [1,7,2,3,4,5,6] => ? = 5
{{1,2,3},{4},{5,7},{6}}
=> [2,3,1,4,7,6,5] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => ? = 6
{{1,2,4,7},{3,5,6}}
=> [2,4,5,7,6,3,1] => [1,2,4,7,3,5,6] => [1,4,7,2,3,5,6] => ? = 4
{{1,2,4,7},{3,5},{6}}
=> [2,4,5,7,3,6,1] => [1,2,4,7,3,5,6] => [1,4,7,2,3,5,6] => ? = 4
{{1,2,4},{3,5,7},{6}}
=> [2,4,5,1,7,6,3] => [1,2,4,3,5,7,6] => [4,1,2,7,3,5,6] => ? = 9
{{1,2,4,7},{3},{5,6}}
=> [2,4,3,7,6,5,1] => [1,2,4,7,3,5,6] => [1,4,7,2,3,5,6] => ? = 4
{{1,2,4,7},{3},{5},{6}}
=> [2,4,3,7,5,6,1] => [1,2,4,7,3,5,6] => [1,4,7,2,3,5,6] => ? = 4
{{1,2,4},{3},{5,7},{6}}
=> [2,4,3,1,7,6,5] => [1,2,4,3,5,7,6] => [4,1,2,7,3,5,6] => ? = 9
{{1,2,5,7},{3,4,6}}
=> [2,5,4,6,7,3,1] => [1,2,5,7,3,4,6] => [1,5,7,2,3,4,6] => ? = 4
{{1,2,5,7},{3,4},{6}}
=> [2,5,4,3,7,6,1] => [1,2,5,7,3,4,6] => [1,5,7,2,3,4,6] => ? = 4
{{1,2,6,7},{3,4,5}}
=> [2,6,4,5,3,7,1] => [1,2,6,7,3,4,5] => [1,6,7,2,3,4,5] => ? = 4
{{1,2},{3,4,5,7},{6}}
=> [2,1,4,5,7,6,3] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => ? = 6
{{1,2,6,7},{3,4},{5}}
=> [2,6,4,3,5,7,1] => [1,2,6,7,3,4,5] => [1,6,7,2,3,4,5] => ? = 4
{{1,2},{3,4,6,7},{5}}
=> [2,1,4,6,5,7,3] => [1,2,3,4,6,7,5] => [6,1,2,3,4,5,7] => ? = 6
{{1,2},{3,4,6},{5,7}}
=> [2,1,4,6,7,3,5] => [1,2,3,4,6,5,7] => [1,6,2,3,4,5,7] => ? = 5
{{1,2},{3,4,6},{5},{7}}
=> [2,1,4,6,5,3,7] => [1,2,3,4,6,5,7] => [1,6,2,3,4,5,7] => ? = 5
{{1,2},{3,4,7},{5,6}}
=> [2,1,4,7,6,5,3] => [1,2,3,4,7,5,6] => [1,7,2,3,4,5,6] => ? = 5
{{1,2},{3,4,7},{5},{6}}
=> [2,1,4,7,5,6,3] => [1,2,3,4,7,5,6] => [1,7,2,3,4,5,6] => ? = 5
{{1,2},{3,4},{5,7},{6}}
=> [2,1,4,3,7,6,5] => [1,2,3,4,5,7,6] => [7,1,2,3,4,5,6] => ? = 6
{{1,2,5},{3,6,7},{4}}
=> [2,5,6,4,1,7,3] => [1,2,5,3,6,7,4] => [5,1,2,6,3,4,7] => ? = 9
{{1,2,5},{3,6},{4,7}}
=> [2,5,6,7,1,3,4] => [1,2,5,3,6,4,7] => [1,5,2,6,3,4,7] => ? = 8
{{1,2,5},{3,6},{4},{7}}
=> [2,5,6,4,1,3,7] => [1,2,5,3,6,4,7] => [1,5,2,6,3,4,7] => ? = 8
{{1,2,5,7},{3},{4,6}}
=> [2,5,3,6,7,4,1] => [1,2,5,7,3,4,6] => [1,5,7,2,3,4,6] => ? = 4
{{1,2,5,7},{3},{4},{6}}
=> [2,5,3,4,7,6,1] => [1,2,5,7,3,4,6] => [1,5,7,2,3,4,6] => ? = 4
{{1,2},{3,5,6,7},{4}}
=> [2,1,5,4,6,7,3] => [1,2,3,5,6,7,4] => [5,1,2,3,4,6,7] => ? = 6
{{1,2},{3,5,6},{4,7}}
=> [2,1,5,7,6,3,4] => [1,2,3,5,6,4,7] => [1,5,2,3,4,6,7] => ? = 5
{{1,2},{3,5,6},{4},{7}}
=> [2,1,5,4,6,3,7] => [1,2,3,5,6,4,7] => [1,5,2,3,4,6,7] => ? = 5
{{1,2},{3,5,7},{4,6}}
=> [2,1,5,6,7,4,3] => [1,2,3,5,7,4,6] => [5,7,1,2,3,4,6] => ? = 5
Description
The comajor index of a permutation.
This is, $\operatorname{comaj}(\pi) = \sum_{i \in \operatorname{Des}(\pi)} (n-i)$ for a permutation $\pi$ of length $n$.
Matching statistic: St000004
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St000004: Permutations ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 57%
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St000004: Permutations ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 57%
Values
{{1}}
=> [1] => [1] => 0
{{1,2}}
=> [2,1] => [1,2] => 0
{{1},{2}}
=> [1,2] => [1,2] => 0
{{1,2,3}}
=> [2,3,1] => [1,2,3] => 0
{{1,2},{3}}
=> [2,1,3] => [1,2,3] => 0
{{1,3},{2}}
=> [3,2,1] => [1,3,2] => 2
{{1},{2,3}}
=> [1,3,2] => [1,2,3] => 0
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
=> [2,3,4,1] => [1,2,3,4] => 0
{{1,2,3},{4}}
=> [2,3,1,4] => [1,2,3,4] => 0
{{1,2,4},{3}}
=> [2,4,3,1] => [1,2,4,3] => 3
{{1,2},{3,4}}
=> [2,1,4,3] => [1,2,3,4] => 0
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,2,3,4] => 0
{{1,3,4},{2}}
=> [3,2,4,1] => [1,3,4,2] => 3
{{1,3},{2,4}}
=> [3,4,1,2] => [1,3,2,4] => 2
{{1,3},{2},{4}}
=> [3,2,1,4] => [1,3,2,4] => 2
{{1,4},{2,3}}
=> [4,3,2,1] => [1,4,2,3] => 2
{{1},{2,3,4}}
=> [1,3,4,2] => [1,2,3,4] => 0
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,2,3,4] => 0
{{1,4},{2},{3}}
=> [4,2,3,1] => [1,4,2,3] => 2
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,2,4,3] => 3
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,3,4] => 0
{{1},{2},{3},{4}}
=> [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}}
=> [2,3,4,5,1] => [1,2,3,4,5] => 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,2,3,4,5] => 0
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,2,3,5,4] => 4
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,2,3,4,5] => 0
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,2,3,4,5] => 0
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,2,4,5,3] => 4
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,2,4,3,5] => 3
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,2,4,3,5] => 3
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,2,5,3,4] => 3
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,2,3,4,5] => 0
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,2,3,4,5] => 0
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,2,5,3,4] => 3
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,2,3,5,4] => 4
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,2,3,4,5] => 0
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [1,2,3,4,5] => 0
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [1,3,4,5,2] => 4
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [1,3,4,2,5] => 3
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,3,4,2,5] => 3
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [1,3,5,2,4] => 3
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [1,3,2,4,5] => 2
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [1,3,2,4,5] => 2
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [1,3,5,2,4] => 3
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [1,3,2,5,4] => 6
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [1,3,2,4,5] => 2
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,3,2,4,5] => 2
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [1,4,5,2,3] => 3
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [1,4,2,3,5] => 2
{{1,2,3,4,5,6,7}}
=> [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,4,5,6},{7}}
=> [2,3,4,5,6,1,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,4,5,7},{6}}
=> [2,3,4,5,7,6,1] => [1,2,3,4,5,7,6] => ? = 6
{{1,2,3,4,5},{6,7}}
=> [2,3,4,5,1,7,6] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,4,5},{6},{7}}
=> [2,3,4,5,1,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,4,6,7},{5}}
=> [2,3,4,6,5,7,1] => [1,2,3,4,6,7,5] => ? = 6
{{1,2,3,4,6},{5,7}}
=> [2,3,4,6,7,1,5] => [1,2,3,4,6,5,7] => ? = 5
{{1,2,3,4,6},{5},{7}}
=> [2,3,4,6,5,1,7] => [1,2,3,4,6,5,7] => ? = 5
{{1,2,3,4,7},{5,6}}
=> [2,3,4,7,6,5,1] => [1,2,3,4,7,5,6] => ? = 5
{{1,2,3,4},{5,6,7}}
=> [2,3,4,1,6,7,5] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,4},{5,6},{7}}
=> [2,3,4,1,6,5,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,4,7},{5},{6}}
=> [2,3,4,7,5,6,1] => [1,2,3,4,7,5,6] => ? = 5
{{1,2,3,4},{5,7},{6}}
=> [2,3,4,1,7,6,5] => [1,2,3,4,5,7,6] => ? = 6
{{1,2,3,4},{5},{6,7}}
=> [2,3,4,1,5,7,6] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,4},{5},{6},{7}}
=> [2,3,4,1,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,5,6,7},{4}}
=> [2,3,5,4,6,7,1] => [1,2,3,5,6,7,4] => ? = 6
{{1,2,3,5,6},{4,7}}
=> [2,3,5,7,6,1,4] => [1,2,3,5,6,4,7] => ? = 5
{{1,2,3,5,6},{4},{7}}
=> [2,3,5,4,6,1,7] => [1,2,3,5,6,4,7] => ? = 5
{{1,2,3,5,7},{4,6}}
=> [2,3,5,6,7,4,1] => [1,2,3,5,7,4,6] => ? = 5
{{1,2,3,5},{4,6,7}}
=> [2,3,5,6,1,7,4] => [1,2,3,5,4,6,7] => ? = 4
{{1,2,3,5},{4,6},{7}}
=> [2,3,5,6,1,4,7] => [1,2,3,5,4,6,7] => ? = 4
{{1,2,3,5,7},{4},{6}}
=> [2,3,5,4,7,6,1] => [1,2,3,5,7,4,6] => ? = 5
{{1,2,3,5},{4,7},{6}}
=> [2,3,5,7,1,6,4] => [1,2,3,5,4,7,6] => ? = 10
{{1,2,3,5},{4},{6,7}}
=> [2,3,5,4,1,7,6] => [1,2,3,5,4,6,7] => ? = 4
{{1,2,3,5},{4},{6},{7}}
=> [2,3,5,4,1,6,7] => [1,2,3,5,4,6,7] => ? = 4
{{1,2,3,6,7},{4,5}}
=> [2,3,6,5,4,7,1] => [1,2,3,6,7,4,5] => ? = 5
{{1,2,3},{4,5,6,7}}
=> [2,3,1,5,6,7,4] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3},{4,5,6},{7}}
=> [2,3,1,5,6,4,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3},{4,5,7},{6}}
=> [2,3,1,5,7,6,4] => [1,2,3,4,5,7,6] => ? = 6
{{1,2,3},{4,5},{6,7}}
=> [2,3,1,5,4,7,6] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3},{4,5},{6},{7}}
=> [2,3,1,5,4,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,6,7},{4},{5}}
=> [2,3,6,4,5,7,1] => [1,2,3,6,7,4,5] => ? = 5
{{1,2,3,6},{4,7},{5}}
=> [2,3,6,7,5,1,4] => [1,2,3,6,4,7,5] => ? = 10
{{1,2,3},{4,6,7},{5}}
=> [2,3,1,6,5,7,4] => [1,2,3,4,6,7,5] => ? = 6
{{1,2,3},{4,6},{5,7}}
=> [2,3,1,6,7,4,5] => [1,2,3,4,6,5,7] => ? = 5
{{1,2,3},{4,6},{5},{7}}
=> [2,3,1,6,5,4,7] => [1,2,3,4,6,5,7] => ? = 5
{{1,2,3},{4,7},{5,6}}
=> [2,3,1,7,6,5,4] => [1,2,3,4,7,5,6] => ? = 5
{{1,2,3},{4},{5,6,7}}
=> [2,3,1,4,6,7,5] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3},{4},{5,6},{7}}
=> [2,3,1,4,6,5,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3},{4,7},{5},{6}}
=> [2,3,1,7,5,6,4] => [1,2,3,4,7,5,6] => ? = 5
{{1,2,3},{4},{5,7},{6}}
=> [2,3,1,4,7,6,5] => [1,2,3,4,5,7,6] => ? = 6
{{1,2,3},{4},{5},{6,7}}
=> [2,3,1,4,5,7,6] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3},{4},{5},{6},{7}}
=> [2,3,1,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,4,7},{3,5,6}}
=> [2,4,5,7,6,3,1] => [1,2,4,7,3,5,6] => ? = 4
{{1,2,4},{3,5,6,7}}
=> [2,4,5,1,6,7,3] => [1,2,4,3,5,6,7] => ? = 3
{{1,2,4},{3,5,6},{7}}
=> [2,4,5,1,6,3,7] => [1,2,4,3,5,6,7] => ? = 3
{{1,2,4,7},{3,5},{6}}
=> [2,4,5,7,3,6,1] => [1,2,4,7,3,5,6] => ? = 4
{{1,2,4},{3,5,7},{6}}
=> [2,4,5,1,7,6,3] => [1,2,4,3,5,7,6] => ? = 9
{{1,2,4},{3,5},{6,7}}
=> [2,4,5,1,3,7,6] => [1,2,4,3,5,6,7] => ? = 3
{{1,2,4},{3,5},{6},{7}}
=> [2,4,5,1,3,6,7] => [1,2,4,3,5,6,7] => ? = 3
Description
The major index of a permutation.
This is the sum of the positions of its descents,
$$\operatorname{maj}(\sigma) = \sum_{\sigma(i) > \sigma(i+1)} i.$$
Its generating function is $[n]_q! = [1]_q \cdot [2]_q \dots [n]_q$ for $[k]_q = 1 + q + q^2 + \dots q^{k-1}$.
A statistic equidistributed with the major index is called '''Mahonian statistic'''.
Matching statistic: St000305
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000305: Permutations ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 57%
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000305: Permutations ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 57%
Values
{{1}}
=> [1] => [1] => [1] => 0
{{1,2}}
=> [2,1] => [1,2] => [1,2] => 0
{{1},{2}}
=> [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
=> [2,3,1] => [1,2,3] => [1,2,3] => 0
{{1,2},{3}}
=> [2,1,3] => [1,2,3] => [1,2,3] => 0
{{1,3},{2}}
=> [3,2,1] => [1,3,2] => [1,3,2] => 2
{{1},{2,3}}
=> [1,3,2] => [1,2,3] => [1,2,3] => 0
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
=> [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3},{4}}
=> [2,3,1,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,4},{3}}
=> [2,4,3,1] => [1,2,4,3] => [1,2,4,3] => 3
{{1,2},{3,4}}
=> [2,1,4,3] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,3,4},{2}}
=> [3,2,4,1] => [1,3,4,2] => [1,4,2,3] => 3
{{1,3},{2,4}}
=> [3,4,1,2] => [1,3,2,4] => [1,3,2,4] => 2
{{1,3},{2},{4}}
=> [3,2,1,4] => [1,3,2,4] => [1,3,2,4] => 2
{{1,4},{2,3}}
=> [4,3,2,1] => [1,4,2,3] => [1,3,4,2] => 2
{{1},{2,3,4}}
=> [1,3,4,2] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,4},{2},{3}}
=> [4,2,3,1] => [1,4,2,3] => [1,3,4,2] => 2
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,2,4,3] => [1,2,4,3] => 3
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,3,4] => [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}}
=> [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,2,3,5,4] => [1,2,3,5,4] => 4
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,2,4,5,3] => [1,2,5,3,4] => 4
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,2,4,3,5] => [1,2,4,3,5] => 3
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,2,4,3,5] => [1,2,4,3,5] => 3
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,2,5,3,4] => [1,2,4,5,3] => 3
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,2,5,3,4] => [1,2,4,5,3] => 3
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,2,3,5,4] => [1,2,3,5,4] => 4
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [1,3,4,5,2] => [1,5,2,3,4] => 4
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [1,3,4,2,5] => [1,4,2,3,5] => 3
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,3,4,2,5] => [1,4,2,3,5] => 3
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [1,3,5,2,4] => [1,4,2,5,3] => 3
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [1,3,2,4,5] => [1,3,2,4,5] => 2
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [1,3,2,4,5] => [1,3,2,4,5] => 2
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [1,3,5,2,4] => [1,4,2,5,3] => 3
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [1,3,2,5,4] => [1,3,2,5,4] => 6
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [1,3,2,4,5] => [1,3,2,4,5] => 2
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 2
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [1,4,5,2,3] => [1,4,5,2,3] => 3
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [1,4,2,3,5] => [1,3,4,2,5] => 2
{{1,2,3,4,5,6,7}}
=> [2,3,4,5,6,7,1] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,4,5,6},{7}}
=> [2,3,4,5,6,1,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,4,5,7},{6}}
=> [2,3,4,5,7,6,1] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => ? = 6
{{1,2,3,4,5},{6,7}}
=> [2,3,4,5,1,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,4,5},{6},{7}}
=> [2,3,4,5,1,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,4,6,7},{5}}
=> [2,3,4,6,5,7,1] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => ? = 6
{{1,2,3,4,6},{5,7}}
=> [2,3,4,6,7,1,5] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => ? = 5
{{1,2,3,4,6},{5},{7}}
=> [2,3,4,6,5,1,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => ? = 5
{{1,2,3,4,7},{5,6}}
=> [2,3,4,7,6,5,1] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => ? = 5
{{1,2,3,4},{5,6,7}}
=> [2,3,4,1,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,4},{5,6},{7}}
=> [2,3,4,1,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,4,7},{5},{6}}
=> [2,3,4,7,5,6,1] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => ? = 5
{{1,2,3,4},{5,7},{6}}
=> [2,3,4,1,7,6,5] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => ? = 6
{{1,2,3,4},{5},{6,7}}
=> [2,3,4,1,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,4},{5},{6},{7}}
=> [2,3,4,1,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,5,6,7},{4}}
=> [2,3,5,4,6,7,1] => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => ? = 6
{{1,2,3,5,6},{4,7}}
=> [2,3,5,7,6,1,4] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => ? = 5
{{1,2,3,5,6},{4},{7}}
=> [2,3,5,4,6,1,7] => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => ? = 5
{{1,2,3,5,7},{4,6}}
=> [2,3,5,6,7,4,1] => [1,2,3,5,7,4,6] => [1,2,3,6,4,7,5] => ? = 5
{{1,2,3,5},{4,6,7}}
=> [2,3,5,6,1,7,4] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => ? = 4
{{1,2,3,5},{4,6},{7}}
=> [2,3,5,6,1,4,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => ? = 4
{{1,2,3,5,7},{4},{6}}
=> [2,3,5,4,7,6,1] => [1,2,3,5,7,4,6] => [1,2,3,6,4,7,5] => ? = 5
{{1,2,3,5},{4,7},{6}}
=> [2,3,5,7,1,6,4] => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => ? = 10
{{1,2,3,5},{4},{6,7}}
=> [2,3,5,4,1,7,6] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => ? = 4
{{1,2,3,5},{4},{6},{7}}
=> [2,3,5,4,1,6,7] => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => ? = 4
{{1,2,3,6,7},{4,5}}
=> [2,3,6,5,4,7,1] => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => ? = 5
{{1,2,3},{4,5,6,7}}
=> [2,3,1,5,6,7,4] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3},{4,5,6},{7}}
=> [2,3,1,5,6,4,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3},{4,5,7},{6}}
=> [2,3,1,5,7,6,4] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => ? = 6
{{1,2,3},{4,5},{6,7}}
=> [2,3,1,5,4,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3},{4,5},{6},{7}}
=> [2,3,1,5,4,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3,6,7},{4},{5}}
=> [2,3,6,4,5,7,1] => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => ? = 5
{{1,2,3,6},{4,7},{5}}
=> [2,3,6,7,5,1,4] => [1,2,3,6,4,7,5] => [1,2,3,5,7,4,6] => ? = 10
{{1,2,3},{4,6,7},{5}}
=> [2,3,1,6,5,7,4] => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => ? = 6
{{1,2,3},{4,6},{5,7}}
=> [2,3,1,6,7,4,5] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => ? = 5
{{1,2,3},{4,6},{5},{7}}
=> [2,3,1,6,5,4,7] => [1,2,3,4,6,5,7] => [1,2,3,4,6,5,7] => ? = 5
{{1,2,3},{4,7},{5,6}}
=> [2,3,1,7,6,5,4] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => ? = 5
{{1,2,3},{4},{5,6,7}}
=> [2,3,1,4,6,7,5] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3},{4},{5,6},{7}}
=> [2,3,1,4,6,5,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3},{4,7},{5},{6}}
=> [2,3,1,7,5,6,4] => [1,2,3,4,7,5,6] => [1,2,3,4,6,7,5] => ? = 5
{{1,2,3},{4},{5,7},{6}}
=> [2,3,1,4,7,6,5] => [1,2,3,4,5,7,6] => [1,2,3,4,5,7,6] => ? = 6
{{1,2,3},{4},{5},{6,7}}
=> [2,3,1,4,5,7,6] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,3},{4},{5},{6},{7}}
=> [2,3,1,4,5,6,7] => [1,2,3,4,5,6,7] => [1,2,3,4,5,6,7] => ? = 0
{{1,2,4,7},{3,5,6}}
=> [2,4,5,7,6,3,1] => [1,2,4,7,3,5,6] => [1,2,5,3,6,7,4] => ? = 4
{{1,2,4},{3,5,6,7}}
=> [2,4,5,1,6,7,3] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => ? = 3
{{1,2,4},{3,5,6},{7}}
=> [2,4,5,1,6,3,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => ? = 3
{{1,2,4,7},{3,5},{6}}
=> [2,4,5,7,3,6,1] => [1,2,4,7,3,5,6] => [1,2,5,3,6,7,4] => ? = 4
{{1,2,4},{3,5,7},{6}}
=> [2,4,5,1,7,6,3] => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => ? = 9
{{1,2,4},{3,5},{6,7}}
=> [2,4,5,1,3,7,6] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => ? = 3
{{1,2,4},{3,5},{6},{7}}
=> [2,4,5,1,3,6,7] => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => ? = 3
Description
The inverse major index of a permutation.
This is the major index [[St000004]] of the inverse permutation [[Mp00066]].
Matching statistic: St001207
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 21%
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 21%
Values
{{1}}
=> [1] => [1] => [1] => ? = 0
{{1,2}}
=> [2,1] => [1,2] => [1,2] => 0
{{1},{2}}
=> [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
=> [2,3,1] => [1,2,3] => [1,2,3] => 0
{{1,2},{3}}
=> [2,1,3] => [1,2,3] => [1,2,3] => 0
{{1,3},{2}}
=> [3,2,1] => [1,3,2] => [3,1,2] => 2
{{1},{2,3}}
=> [1,3,2] => [1,2,3] => [1,2,3] => 0
{{1},{2},{3}}
=> [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
=> [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3},{4}}
=> [2,3,1,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,4},{3}}
=> [2,4,3,1] => [1,2,4,3] => [4,1,2,3] => 3
{{1,2},{3,4}}
=> [2,1,4,3] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2},{3},{4}}
=> [2,1,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,3,4},{2}}
=> [3,2,4,1] => [1,3,4,2] => [3,4,1,2] => 3
{{1,3},{2,4}}
=> [3,4,1,2] => [1,3,2,4] => [3,1,2,4] => 2
{{1,3},{2},{4}}
=> [3,2,1,4] => [1,3,2,4] => [3,1,2,4] => 2
{{1,4},{2,3}}
=> [4,3,2,1] => [1,4,2,3] => [1,4,2,3] => 2
{{1},{2,3,4}}
=> [1,3,4,2] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2,3},{4}}
=> [1,3,2,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,4},{2},{3}}
=> [4,2,3,1] => [1,4,2,3] => [1,4,2,3] => 2
{{1},{2,4},{3}}
=> [1,4,3,2] => [1,2,4,3] => [4,1,2,3] => 3
{{1},{2},{3,4}}
=> [1,2,4,3] => [1,2,3,4] => [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}}
=> [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,2,3,4},{5}}
=> [2,3,4,1,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,2,3,5},{4}}
=> [2,3,5,4,1] => [1,2,3,5,4] => [5,1,2,3,4] => ? = 4
{{1,2,3},{4,5}}
=> [2,3,1,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,2,3},{4},{5}}
=> [2,3,1,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,2,4,5},{3}}
=> [2,4,3,5,1] => [1,2,4,5,3] => [4,5,1,2,3] => ? = 4
{{1,2,4},{3,5}}
=> [2,4,5,1,3] => [1,2,4,3,5] => [4,1,2,3,5] => ? = 3
{{1,2,4},{3},{5}}
=> [2,4,3,1,5] => [1,2,4,3,5] => [4,1,2,3,5] => ? = 3
{{1,2,5},{3,4}}
=> [2,5,4,3,1] => [1,2,5,3,4] => [1,5,2,3,4] => ? = 3
{{1,2},{3,4,5}}
=> [2,1,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,2},{3,4},{5}}
=> [2,1,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,2,5},{3},{4}}
=> [2,5,3,4,1] => [1,2,5,3,4] => [1,5,2,3,4] => ? = 3
{{1,2},{3,5},{4}}
=> [2,1,5,4,3] => [1,2,3,5,4] => [5,1,2,3,4] => ? = 4
{{1,2},{3},{4,5}}
=> [2,1,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,2},{3},{4},{5}}
=> [2,1,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,3,4,5},{2}}
=> [3,2,4,5,1] => [1,3,4,5,2] => [3,4,5,1,2] => ? = 4
{{1,3,4},{2,5}}
=> [3,5,4,1,2] => [1,3,4,2,5] => [3,4,1,2,5] => ? = 3
{{1,3,4},{2},{5}}
=> [3,2,4,1,5] => [1,3,4,2,5] => [3,4,1,2,5] => ? = 3
{{1,3,5},{2,4}}
=> [3,4,5,2,1] => [1,3,5,2,4] => [5,3,1,2,4] => ? = 3
{{1,3},{2,4,5}}
=> [3,4,1,5,2] => [1,3,2,4,5] => [3,1,2,4,5] => ? = 2
{{1,3},{2,4},{5}}
=> [3,4,1,2,5] => [1,3,2,4,5] => [3,1,2,4,5] => ? = 2
{{1,3,5},{2},{4}}
=> [3,2,5,4,1] => [1,3,5,2,4] => [5,3,1,2,4] => ? = 3
{{1,3},{2,5},{4}}
=> [3,5,1,4,2] => [1,3,2,5,4] => [3,5,1,2,4] => ? = 6
{{1,3},{2},{4,5}}
=> [3,2,1,5,4] => [1,3,2,4,5] => [3,1,2,4,5] => ? = 2
{{1,3},{2},{4},{5}}
=> [3,2,1,4,5] => [1,3,2,4,5] => [3,1,2,4,5] => ? = 2
{{1,4,5},{2,3}}
=> [4,3,2,5,1] => [1,4,5,2,3] => [4,1,5,2,3] => ? = 3
{{1,4},{2,3,5}}
=> [4,3,5,1,2] => [1,4,2,3,5] => [1,4,2,3,5] => ? = 2
{{1,4},{2,3},{5}}
=> [4,3,2,1,5] => [1,4,2,3,5] => [1,4,2,3,5] => ? = 2
{{1,5},{2,3,4}}
=> [5,3,4,2,1] => [1,5,2,3,4] => [1,2,5,3,4] => ? = 2
{{1},{2,3,4,5}}
=> [1,3,4,5,2] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1},{2,3,4},{5}}
=> [1,3,4,2,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,5},{2,3},{4}}
=> [5,3,2,4,1] => [1,5,2,3,4] => [1,2,5,3,4] => ? = 2
{{1},{2,3,5},{4}}
=> [1,3,5,4,2] => [1,2,3,5,4] => [5,1,2,3,4] => ? = 4
{{1},{2,3},{4,5}}
=> [1,3,2,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1},{2,3},{4},{5}}
=> [1,3,2,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,4,5},{2},{3}}
=> [4,2,3,5,1] => [1,4,5,2,3] => [4,1,5,2,3] => ? = 3
{{1,4},{2,5},{3}}
=> [4,5,3,1,2] => [1,4,2,5,3] => [1,4,5,2,3] => ? = 6
{{1,4},{2},{3,5}}
=> [4,2,5,1,3] => [1,4,2,3,5] => [1,4,2,3,5] => ? = 2
{{1,4},{2},{3},{5}}
=> [4,2,3,1,5] => [1,4,2,3,5] => [1,4,2,3,5] => ? = 2
{{1,5},{2,4},{3}}
=> [5,4,3,2,1] => [1,5,2,4,3] => [5,1,4,2,3] => ? = 6
{{1},{2,4,5},{3}}
=> [1,4,3,5,2] => [1,2,4,5,3] => [4,5,1,2,3] => ? = 4
{{1},{2,4},{3,5}}
=> [1,4,5,2,3] => [1,2,4,3,5] => [4,1,2,3,5] => ? = 3
{{1},{2,4},{3},{5}}
=> [1,4,3,2,5] => [1,2,4,3,5] => [4,1,2,3,5] => ? = 3
{{1,5},{2},{3,4}}
=> [5,2,4,3,1] => [1,5,2,3,4] => [1,2,5,3,4] => ? = 2
{{1},{2,5},{3,4}}
=> [1,5,4,3,2] => [1,2,5,3,4] => [1,5,2,3,4] => ? = 3
{{1},{2},{3,4,5}}
=> [1,2,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1},{2},{3,4},{5}}
=> [1,2,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,5},{2},{3},{4}}
=> [5,2,3,4,1] => [1,5,2,3,4] => [1,2,5,3,4] => ? = 2
{{1},{2,5},{3},{4}}
=> [1,5,3,4,2] => [1,2,5,3,4] => [1,5,2,3,4] => ? = 3
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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