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Matching statistic: St001379
St001379: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[1,2] => 0
[2,1] => 2
[1,2,3] => 0
[1,3,2] => 3
[2,1,3] => 2
[2,3,1] => 4
[3,1,2] => 3
[3,2,1] => 6
[1,2,3,4] => 0
[1,2,4,3] => 4
[1,3,2,4] => 3
[1,3,4,2] => 5
[1,4,2,3] => 4
[1,4,3,2] => 8
[2,1,3,4] => 2
[2,1,4,3] => 6
[2,3,1,4] => 4
[2,3,4,1] => 6
[2,4,1,3] => 5
[2,4,3,1] => 9
[3,1,2,4] => 3
[3,1,4,2] => 7
[3,2,1,4] => 6
[3,2,4,1] => 8
[3,4,1,2] => 6
[3,4,2,1] => 10
[4,1,2,3] => 4
[4,1,3,2] => 8
[4,2,1,3] => 7
[4,2,3,1] => 9
[4,3,1,2] => 8
[4,3,2,1] => 12
[1,2,3,4,5] => 0
[1,2,3,5,4] => 5
[1,2,4,3,5] => 4
[1,2,4,5,3] => 6
[1,2,5,3,4] => 5
[1,2,5,4,3] => 10
[1,3,2,4,5] => 3
[1,3,2,5,4] => 8
[1,3,4,2,5] => 5
[1,3,4,5,2] => 7
[1,3,5,2,4] => 6
[1,3,5,4,2] => 11
[1,4,2,3,5] => 4
[1,4,2,5,3] => 9
[1,4,3,2,5] => 8
[1,4,3,5,2] => 10
[1,4,5,2,3] => 7
Description
The number of inversions plus the major index of a permutation.
This is, the sum of [[St000004]] and [[St000018]].
Matching statistic: St000825
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00066: Permutations —inverse⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000825: Permutations ⟶ ℤResult quality: 80% ●values known / values provided: 80%●distinct values known / distinct values provided: 97%
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000825: Permutations ⟶ ℤResult quality: 80% ●values known / values provided: 80%●distinct values known / distinct values provided: 97%
Values
[1] => [1] => [1] => [1] => 0
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => [2,1] => 2
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [3,1,2] => [2,3,1] => 3
[2,1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 2
[2,3,1] => [3,1,2] => [1,3,2] => [1,3,2] => 4
[3,1,2] => [2,3,1] => [2,3,1] => [3,1,2] => 3
[3,2,1] => [3,2,1] => [3,2,1] => [3,2,1] => 6
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [4,1,2,3] => [2,3,4,1] => 4
[1,3,2,4] => [1,3,2,4] => [3,1,2,4] => [2,3,1,4] => 3
[1,3,4,2] => [1,4,2,3] => [1,4,2,3] => [1,3,4,2] => 5
[1,4,2,3] => [1,3,4,2] => [3,4,1,2] => [3,4,1,2] => 4
[1,4,3,2] => [1,4,3,2] => [4,3,1,2] => [3,4,2,1] => 8
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 2
[2,1,4,3] => [2,1,4,3] => [2,4,1,3] => [3,1,4,2] => 6
[2,3,1,4] => [3,1,2,4] => [1,3,2,4] => [1,3,2,4] => 4
[2,3,4,1] => [4,1,2,3] => [1,2,4,3] => [1,2,4,3] => 6
[2,4,1,3] => [3,1,4,2] => [1,3,4,2] => [1,4,2,3] => 5
[2,4,3,1] => [4,1,3,2] => [4,1,3,2] => [2,4,3,1] => 9
[3,1,2,4] => [2,3,1,4] => [2,3,1,4] => [3,1,2,4] => 3
[3,1,4,2] => [2,4,1,3] => [4,2,1,3] => [3,2,4,1] => 7
[3,2,1,4] => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 6
[3,2,4,1] => [4,2,1,3] => [2,1,4,3] => [2,1,4,3] => 8
[3,4,1,2] => [3,4,1,2] => [3,1,4,2] => [2,4,1,3] => 6
[3,4,2,1] => [4,3,1,2] => [1,4,3,2] => [1,4,3,2] => 10
[4,1,2,3] => [2,3,4,1] => [2,3,4,1] => [4,1,2,3] => 4
[4,1,3,2] => [2,4,3,1] => [4,2,3,1] => [4,2,3,1] => 8
[4,2,1,3] => [3,2,4,1] => [3,2,4,1] => [4,2,1,3] => 7
[4,2,3,1] => [4,2,3,1] => [2,4,3,1] => [4,1,3,2] => 9
[4,3,1,2] => [3,4,2,1] => [3,4,2,1] => [4,3,1,2] => 8
[4,3,2,1] => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 12
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => [2,3,4,5,1] => 5
[1,2,4,3,5] => [1,2,4,3,5] => [4,1,2,3,5] => [2,3,4,1,5] => 4
[1,2,4,5,3] => [1,2,5,3,4] => [1,5,2,3,4] => [1,3,4,5,2] => 6
[1,2,5,3,4] => [1,2,4,5,3] => [4,5,1,2,3] => [3,4,5,1,2] => 5
[1,2,5,4,3] => [1,2,5,4,3] => [5,4,1,2,3] => [3,4,5,2,1] => 10
[1,3,2,4,5] => [1,3,2,4,5] => [3,1,2,4,5] => [2,3,1,4,5] => 3
[1,3,2,5,4] => [1,3,2,5,4] => [3,5,1,2,4] => [3,4,1,5,2] => 8
[1,3,4,2,5] => [1,4,2,3,5] => [1,4,2,3,5] => [1,3,4,2,5] => 5
[1,3,4,5,2] => [1,5,2,3,4] => [1,2,5,3,4] => [1,2,4,5,3] => 7
[1,3,5,2,4] => [1,4,2,5,3] => [1,4,5,2,3] => [1,4,5,2,3] => 6
[1,3,5,4,2] => [1,5,2,4,3] => [5,1,4,2,3] => [2,4,5,3,1] => 11
[1,4,2,3,5] => [1,3,4,2,5] => [3,4,1,2,5] => [3,4,1,2,5] => 4
[1,4,2,5,3] => [1,3,5,2,4] => [5,3,1,2,4] => [3,4,2,5,1] => 9
[1,4,3,2,5] => [1,4,3,2,5] => [4,3,1,2,5] => [3,4,2,1,5] => 8
[1,4,3,5,2] => [1,5,3,2,4] => [5,1,3,2,4] => [2,4,3,5,1] => 10
[1,4,5,2,3] => [1,4,5,2,3] => [4,1,5,2,3] => [2,4,5,1,3] => 7
[1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => [7,6,1,2,3,4,5] => [3,4,5,6,7,2,1] => ? = 14
[1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => [5,7,1,2,3,4,6] => [3,4,5,6,1,7,2] => ? = 12
[1,2,3,5,7,6,4] => [1,2,3,7,4,6,5] => [7,1,6,2,3,4,5] => [2,4,5,6,7,3,1] => ? = 15
[1,2,3,6,4,5,7] => [1,2,3,5,6,4,7] => [5,6,1,2,3,4,7] => [3,4,5,6,1,2,7] => ? = 6
[1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => [6,5,1,2,3,4,7] => [3,4,5,6,2,1,7] => ? = 12
[1,2,3,6,5,7,4] => [1,2,3,7,5,4,6] => [7,1,5,2,3,4,6] => [2,4,5,6,3,7,1] => ? = 14
[1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => [6,1,7,2,3,4,5] => [2,4,5,6,7,1,3] => ? = 9
[1,2,3,7,4,5,6] => [1,2,3,5,6,7,4] => [5,6,7,1,2,3,4] => [4,5,6,7,1,2,3] => ? = 7
[1,2,3,7,4,6,5] => [1,2,3,5,7,6,4] => [7,5,6,1,2,3,4] => [4,5,6,7,2,3,1] => ? = 14
[1,2,3,7,5,4,6] => [1,2,3,6,5,7,4] => [6,5,7,1,2,3,4] => [4,5,6,7,2,1,3] => ? = 13
[1,2,3,7,5,6,4] => [1,2,3,7,5,6,4] => [5,7,6,1,2,3,4] => [4,5,6,7,1,3,2] => ? = 15
[1,2,3,7,6,4,5] => [1,2,3,6,7,5,4] => [6,7,5,1,2,3,4] => [4,5,6,7,3,1,2] => ? = 14
[1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => [4,5,6,7,3,2,1] => ? = 21
[1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => [4,7,1,2,3,5,6] => [3,4,5,1,6,7,2] => ? = 11
[1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => [4,6,1,2,3,5,7] => [3,4,5,1,6,2,7] => ? = 10
[1,2,4,3,7,5,6] => [1,2,4,3,6,7,5] => [4,6,7,1,2,3,5] => [4,5,6,1,7,2,3] => ? = 11
[1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => [7,4,6,1,2,3,5] => [4,5,6,2,7,3,1] => ? = 18
[1,2,4,5,7,6,3] => [1,2,7,3,4,6,5] => [7,1,2,6,3,4,5] => [2,3,5,6,7,4,1] => ? = 16
[1,2,4,6,3,7,5] => [1,2,5,3,7,4,6] => [5,1,7,2,3,4,6] => [2,4,5,6,1,7,3] => ? = 14
[1,2,4,6,5,3,7] => [1,2,6,3,5,4,7] => [6,1,5,2,3,4,7] => [2,4,5,6,3,1,7] => ? = 13
[1,2,4,6,5,7,3] => [1,2,7,3,5,4,6] => [7,1,2,5,3,4,6] => [2,3,5,6,4,7,1] => ? = 15
[1,2,4,7,3,6,5] => [1,2,5,3,7,6,4] => [7,1,5,6,2,3,4] => [2,5,6,7,3,4,1] => ? = 15
[1,2,4,7,5,3,6] => [1,2,6,3,5,7,4] => [6,1,5,7,2,3,4] => [2,5,6,7,3,1,4] => ? = 14
[1,2,4,7,5,6,3] => [1,2,7,3,5,6,4] => [1,7,5,6,2,3,4] => [1,5,6,7,3,4,2] => ? = 16
[1,2,4,7,6,3,5] => [1,2,6,3,7,5,4] => [6,7,1,5,2,3,4] => [3,5,6,7,4,1,2] => ? = 15
[1,2,4,7,6,5,3] => [1,2,7,3,6,5,4] => [7,6,1,5,2,3,4] => [3,5,6,7,4,2,1] => ? = 22
[1,2,5,3,4,6,7] => [1,2,4,5,3,6,7] => [4,5,1,2,3,6,7] => [3,4,5,1,2,6,7] => ? = 5
[1,2,5,3,4,7,6] => [1,2,4,5,3,7,6] => [4,5,7,1,2,3,6] => [4,5,6,1,2,7,3] => ? = 12
[1,2,5,3,6,4,7] => [1,2,4,6,3,5,7] => [6,4,1,2,3,5,7] => [3,4,5,2,6,1,7] => ? = 11
[1,2,5,3,6,7,4] => [1,2,4,7,3,5,6] => [7,1,4,2,3,5,6] => [2,4,5,3,6,7,1] => ? = 13
[1,2,5,3,7,4,6] => [1,2,4,6,3,7,5] => [6,4,7,1,2,3,5] => [4,5,6,2,7,1,3] => ? = 12
[1,2,5,3,7,6,4] => [1,2,4,7,3,6,5] => [4,7,6,1,2,3,5] => [4,5,6,1,7,3,2] => ? = 19
[1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => [5,4,1,2,3,6,7] => [3,4,5,2,1,6,7] => ? = 10
[1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => [5,4,7,1,2,3,6] => [4,5,6,2,1,7,3] => ? = 17
[1,2,5,4,6,3,7] => [1,2,6,4,3,5,7] => [6,1,4,2,3,5,7] => [2,4,5,3,6,1,7] => ? = 12
[1,2,5,4,6,7,3] => [1,2,7,4,3,5,6] => [7,1,2,4,3,5,6] => [2,3,5,4,6,7,1] => ? = 14
[1,2,5,4,7,3,6] => [1,2,6,4,3,7,5] => [6,1,4,7,2,3,5] => [2,5,6,3,7,1,4] => ? = 13
[1,2,5,4,7,6,3] => [1,2,7,4,3,6,5] => [1,7,4,6,2,3,5] => [1,5,6,3,7,4,2] => ? = 20
[1,2,5,6,3,4,7] => [1,2,5,6,3,4,7] => [5,1,6,2,3,4,7] => [2,4,5,6,1,3,7] => ? = 8
[1,2,5,7,3,4,6] => [1,2,5,6,3,7,4] => [5,1,6,7,2,3,4] => [2,5,6,7,1,3,4] => ? = 9
[1,2,5,7,3,6,4] => [1,2,5,7,3,6,4] => [5,7,1,6,2,3,4] => [3,5,6,7,1,4,2] => ? = 16
[1,2,5,7,4,3,6] => [1,2,6,5,3,7,4] => [1,6,5,7,2,3,4] => [1,5,6,7,3,2,4] => ? = 15
[1,2,5,7,4,6,3] => [1,2,7,5,3,6,4] => [1,5,7,6,2,3,4] => [1,5,6,7,2,4,3] => ? = 17
[1,2,5,7,6,3,4] => [1,2,6,7,3,5,4] => [1,6,7,5,2,3,4] => [1,5,6,7,4,2,3] => ? = 16
[1,2,5,7,6,4,3] => [1,2,7,6,3,5,4] => [7,1,6,5,2,3,4] => [2,5,6,7,4,3,1] => ? = 23
[1,2,6,3,4,7,5] => [1,2,4,5,7,3,6] => [7,4,5,1,2,3,6] => [4,5,6,2,3,7,1] => ? = 13
[1,2,6,3,5,4,7] => [1,2,4,6,5,3,7] => [6,4,5,1,2,3,7] => [4,5,6,2,3,1,7] => ? = 12
[1,2,6,3,5,7,4] => [1,2,4,7,5,3,6] => [4,7,5,1,2,3,6] => [4,5,6,1,3,7,2] => ? = 14
[1,2,6,3,7,4,5] => [1,2,4,6,7,3,5] => [6,7,4,1,2,3,5] => [4,5,6,3,7,1,2] => ? = 13
[1,2,6,3,7,5,4] => [1,2,4,7,6,3,5] => [7,6,4,1,2,3,5] => [4,5,6,3,7,2,1] => ? = 20
Description
The sum of the major and the inverse major index of a permutation.
This statistic is the sum of [[St000004]] and [[St000305]].
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