Your data matches 3 different statistics following compositions of up to 3 maps.
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Matching statistic: St000425
(load all 4 compositions to match this statistic)
Mapping
St000425: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[1,2] => 0
[2,1] => 0
[1,2,3] => 0
[1,3,2] => 1
[2,1,3] => 1
[2,3,1] => 0
[3,1,2] => 0
[3,2,1] => 0
[1,2,3,4] => 0
[1,2,4,3] => 2
[1,3,2,4] => 2
[1,3,4,2] => 2
[1,4,2,3] => 2
[1,4,3,2] => 3
[2,1,3,4] => 2
[2,1,4,3] => 4
[2,3,1,4] => 2
[2,3,4,1] => 0
[2,4,1,3] => 2
[2,4,3,1] => 1
[3,1,2,4] => 2
[3,1,4,2] => 2
[3,2,1,4] => 3
[3,2,4,1] => 1
[3,4,1,2] => 0
[3,4,2,1] => 0
[4,1,2,3] => 0
[4,1,3,2] => 1
[4,2,1,3] => 1
[4,2,3,1] => 0
[4,3,1,2] => 0
[4,3,2,1] => 0
[1,2,3,4,5] => 0
[1,2,3,5,4] => 3
[1,2,4,3,5] => 3
[1,2,4,5,3] => 4
[1,2,5,3,4] => 4
[1,2,5,4,3] => 6
[1,3,2,4,5] => 3
[1,3,2,5,4] => 6
[1,3,4,2,5] => 4
[1,3,4,5,2] => 3
[1,3,5,2,4] => 5
[1,3,5,4,2] => 5
[1,4,2,3,5] => 4
[1,4,2,5,3] => 5
[1,4,3,2,5] => 6
[1,4,3,5,2] => 5
[1,4,5,2,3] => 4
Description
The number of occurrences of the pattern 132 or of the pattern 213 in a permutation.
Matching statistic: St001308
(load all 2 compositions to match this statistic)
Mapping
Mp00064: Permutations —reverse⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St001308: Graphs ⟶ ℤResult quality: 93% ●values known / values provided: 93%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => ([],1)
 => 0
[1,2] => [2,1] => ([(0,1)],2)
 => 0
[2,1] => [1,2] => ([],2)
 => 0
[1,2,3] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 0
[1,3,2] => [2,3,1] => ([(0,2),(1,2)],3)
 => 1
[2,1,3] => [3,1,2] => ([(0,2),(1,2)],3)
 => 1
[2,3,1] => [1,3,2] => ([(1,2)],3)
 => 0
[3,1,2] => [2,1,3] => ([(1,2)],3)
 => 0
[3,2,1] => [1,2,3] => ([],3)
 => 0
[1,2,3,4] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 0
[1,2,4,3] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[1,3,2,4] => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[1,3,4,2] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[1,4,2,3] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
[2,1,3,4] => [4,3,1,2] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[2,1,4,3] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[2,3,1,4] => [4,1,3,2] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[2,3,4,1] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => 0
[2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
 => 2
[2,4,3,1] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => 1
[3,1,2,4] => [4,2,1,3] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
[3,1,4,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
 => 2
[3,2,1,4] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4)
 => 3
[3,2,4,1] => [1,4,2,3] => ([(1,3),(2,3)],4)
 => 1
[3,4,1,2] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => 0
[3,4,2,1] => [1,2,4,3] => ([(2,3)],4)
 => 0
[4,1,2,3] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => 0
[4,1,3,2] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => 1
[4,2,1,3] => [3,1,2,4] => ([(1,3),(2,3)],4)
 => 1
[4,2,3,1] => [1,3,2,4] => ([(2,3)],4)
 => 0
[4,3,1,2] => [2,1,3,4] => ([(2,3)],4)
 => 0
[4,3,2,1] => [1,2,3,4] => ([],4)
 => 0
[1,2,3,4,5] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
[1,2,3,5,4] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[1,2,4,3,5] => [5,3,4,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[1,2,4,5,3] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,2,5,3,4] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,2,5,4,3] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
[1,3,2,4,5] => [5,4,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[1,3,2,5,4] => [4,5,2,3,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 6
[1,3,4,2,5] => [5,2,4,3,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,3,4,5,2] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
[1,3,5,2,4] => [4,2,5,3,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
[1,3,5,4,2] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
[1,4,2,3,5] => [5,3,2,4,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,4,2,5,3] => [3,5,2,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
[1,4,3,2,5] => [5,2,3,4,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6
[1,4,3,5,2] => [2,5,3,4,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 5
[1,4,5,2,3] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 4
[1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 0
[1,2,3,4,5,7,6] => [6,7,5,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5
[1,2,3,4,6,5,7] => [7,5,6,4,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5
[1,2,3,4,6,7,5] => [5,7,6,4,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 8
[1,2,3,4,7,5,6] => [6,5,7,4,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 8
[1,2,3,5,4,6,7] => [7,6,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5
[1,2,3,5,4,7,6] => [6,7,4,5,3,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 10
[1,2,3,5,6,4,7] => [7,4,6,5,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 8
[1,2,3,5,6,7,4] => [4,7,6,5,3,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 9
[1,2,3,5,7,4,6] => [6,4,7,5,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 11
[1,2,3,6,4,5,7] => [7,5,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 8
[1,2,3,6,4,7,5] => [5,7,4,6,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 11
[1,2,3,6,7,4,5] => [5,4,7,6,3,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 12
[1,2,3,7,4,5,6] => [6,5,4,7,3,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 9
[1,2,4,3,5,6,7] => [7,6,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5
[1,2,4,3,5,7,6] => [6,7,5,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 10
[1,2,4,3,6,5,7] => [7,5,6,3,4,2,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 10
[1,2,4,3,6,7,5] => [5,7,6,3,4,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 13
[1,2,4,3,7,5,6] => [6,5,7,3,4,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 13
[1,2,4,5,3,6,7] => [7,6,3,5,4,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 8
[1,2,4,5,3,7,6] => [6,7,3,5,4,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 13
[1,2,4,5,6,3,7] => [7,3,6,5,4,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 9
[1,2,4,5,6,7,3] => [3,7,6,5,4,2,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 8
[1,2,4,5,7,3,6] => [6,3,7,5,4,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 12
[1,2,4,6,3,5,7] => [7,5,3,6,4,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 11
[1,2,4,6,3,7,5] => [5,7,3,6,4,2,1] => ([(0,1),(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 14
[1,2,4,7,3,5,6] => [6,5,3,7,4,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 12
[1,2,5,3,4,6,7] => [7,6,4,3,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 8
[1,2,5,3,4,7,6] => [6,7,4,3,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 13
[1,2,5,3,6,4,7] => [7,4,6,3,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 11
[1,2,5,3,6,7,4] => [4,7,6,3,5,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 12
[1,2,5,3,7,4,6] => [6,4,7,3,5,2,1] => ([(0,1),(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 14
[1,2,5,6,3,4,7] => [7,4,3,6,5,2,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 12
[1,2,6,3,4,5,7] => [7,5,4,3,6,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 9
[1,2,6,3,4,7,5] => [5,7,4,3,6,2,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 12
[1,2,7,3,4,5,6] => [6,5,4,3,7,2,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 8
[1,3,2,4,5,6,7] => [7,6,5,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 5
[1,3,2,4,5,7,6] => [6,7,5,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 10
[1,3,2,4,6,5,7] => [7,5,6,4,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 10
[1,3,2,4,6,7,5] => [5,7,6,4,2,3,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 13
[1,3,2,4,7,5,6] => [6,5,7,4,2,3,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 13
[1,3,2,5,4,6,7] => [7,6,4,5,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 10
[1,3,2,5,4,7,6] => [6,7,4,5,2,3,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 15
[1,3,2,5,6,4,7] => [7,4,6,5,2,3,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 13
[1,3,2,5,6,7,4] => [4,7,6,5,2,3,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 14
[1,3,2,5,7,4,6] => [6,4,7,5,2,3,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 16
[1,3,2,6,4,5,7] => [7,5,4,6,2,3,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 13
[1,3,2,6,4,7,5] => [5,7,4,6,2,3,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 16
[1,3,2,7,4,5,6] => [6,5,4,7,2,3,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,6),(5,6)],7)
 => ? = 14
[1,3,4,2,5,6,7] => [7,6,5,2,4,3,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ? = 8
Description
The number of induced paths on three vertices in a graph.
Matching statistic: St000432
(load all 4 compositions to match this statistic)
Mapping
Mp00069: Permutations —complement⟶ Permutations
St000432: Permutations ⟶ ℤResult quality: 73% ●values known / values provided: 73%●distinct values known / distinct values provided: 75%
Values
[1] => [1] => ? = 0
[1,2] => [2,1] => 0
[2,1] => [1,2] => 0
[1,2,3] => [3,2,1] => 0
[1,3,2] => [3,1,2] => 1
[2,1,3] => [2,3,1] => 1
[2,3,1] => [2,1,3] => 0
[3,1,2] => [1,3,2] => 0
[3,2,1] => [1,2,3] => 0
[1,2,3,4] => [4,3,2,1] => 0
[1,2,4,3] => [4,3,1,2] => 2
[1,3,2,4] => [4,2,3,1] => 2
[1,3,4,2] => [4,2,1,3] => 2
[1,4,2,3] => [4,1,3,2] => 2
[1,4,3,2] => [4,1,2,3] => 3
[2,1,3,4] => [3,4,2,1] => 2
[2,1,4,3] => [3,4,1,2] => 4
[2,3,1,4] => [3,2,4,1] => 2
[2,3,4,1] => [3,2,1,4] => 0
[2,4,1,3] => [3,1,4,2] => 2
[2,4,3,1] => [3,1,2,4] => 1
[3,1,2,4] => [2,4,3,1] => 2
[3,1,4,2] => [2,4,1,3] => 2
[3,2,1,4] => [2,3,4,1] => 3
[3,2,4,1] => [2,3,1,4] => 1
[3,4,1,2] => [2,1,4,3] => 0
[3,4,2,1] => [2,1,3,4] => 0
[4,1,2,3] => [1,4,3,2] => 0
[4,1,3,2] => [1,4,2,3] => 1
[4,2,1,3] => [1,3,4,2] => 1
[4,2,3,1] => [1,3,2,4] => 0
[4,3,1,2] => [1,2,4,3] => 0
[4,3,2,1] => [1,2,3,4] => 0
[1,2,3,4,5] => [5,4,3,2,1] => 0
[1,2,3,5,4] => [5,4,3,1,2] => 3
[1,2,4,3,5] => [5,4,2,3,1] => 3
[1,2,4,5,3] => [5,4,2,1,3] => 4
[1,2,5,3,4] => [5,4,1,3,2] => 4
[1,2,5,4,3] => [5,4,1,2,3] => 6
[1,3,2,4,5] => [5,3,4,2,1] => 3
[1,3,2,5,4] => [5,3,4,1,2] => 6
[1,3,4,2,5] => [5,3,2,4,1] => 4
[1,3,4,5,2] => [5,3,2,1,4] => 3
[1,3,5,2,4] => [5,3,1,4,2] => 5
[1,3,5,4,2] => [5,3,1,2,4] => 5
[1,4,2,3,5] => [5,2,4,3,1] => 4
[1,4,2,5,3] => [5,2,4,1,3] => 5
[1,4,3,2,5] => [5,2,3,4,1] => 6
[1,4,3,5,2] => [5,2,3,1,4] => 5
[1,4,5,2,3] => [5,2,1,4,3] => 4
[1,4,5,3,2] => [5,2,1,3,4] => 5
[1,2,3,4,5,6,7] => [7,6,5,4,3,2,1] => ? = 0
[1,2,3,4,5,7,6] => [7,6,5,4,3,1,2] => ? = 5
[1,2,3,4,6,5,7] => [7,6,5,4,2,3,1] => ? = 5
[1,2,3,4,6,7,5] => [7,6,5,4,2,1,3] => ? = 8
[1,2,3,4,7,5,6] => [7,6,5,4,1,3,2] => ? = 8
[1,2,3,4,7,6,5] => [7,6,5,4,1,2,3] => ? = 12
[1,2,3,5,4,6,7] => [7,6,5,3,4,2,1] => ? = 5
[1,2,3,5,4,7,6] => [7,6,5,3,4,1,2] => ? = 10
[1,2,3,5,6,4,7] => [7,6,5,3,2,4,1] => ? = 8
[1,2,3,5,6,7,4] => [7,6,5,3,2,1,4] => ? = 9
[1,2,3,5,7,4,6] => [7,6,5,3,1,4,2] => ? = 11
[1,2,3,5,7,6,4] => [7,6,5,3,1,2,4] => ? = 13
[1,2,3,6,4,5,7] => [7,6,5,2,4,3,1] => ? = 8
[1,2,3,6,4,7,5] => [7,6,5,2,4,1,3] => ? = 11
[1,2,3,6,5,4,7] => [7,6,5,2,3,4,1] => ? = 12
[1,2,3,6,5,7,4] => [7,6,5,2,3,1,4] => ? = 13
[1,2,3,6,7,4,5] => [7,6,5,2,1,4,3] => ? = 12
[1,2,3,6,7,5,4] => [7,6,5,2,1,3,4] => ? = 15
[1,2,3,7,4,5,6] => [7,6,5,1,4,3,2] => ? = 9
[1,2,3,7,4,6,5] => [7,6,5,1,4,2,3] => ? = 13
[1,2,3,7,5,4,6] => [7,6,5,1,3,4,2] => ? = 13
[1,2,3,7,5,6,4] => [7,6,5,1,3,2,4] => ? = 15
[1,2,3,7,6,4,5] => [7,6,5,1,2,4,3] => ? = 15
[1,2,3,7,6,5,4] => [7,6,5,1,2,3,4] => ? = 18
[1,2,4,3,5,6,7] => [7,6,4,5,3,2,1] => ? = 5
[1,2,4,3,5,7,6] => [7,6,4,5,3,1,2] => ? = 10
[1,2,4,3,6,5,7] => [7,6,4,5,2,3,1] => ? = 10
[1,2,4,3,6,7,5] => [7,6,4,5,2,1,3] => ? = 13
[1,2,4,3,7,5,6] => [7,6,4,5,1,3,2] => ? = 13
[1,2,4,3,7,6,5] => [7,6,4,5,1,2,3] => ? = 17
[1,2,4,5,3,6,7] => [7,6,4,3,5,2,1] => ? = 8
[1,2,4,5,3,7,6] => [7,6,4,3,5,1,2] => ? = 13
[1,2,4,5,6,3,7] => [7,6,4,3,2,5,1] => ? = 9
[1,2,4,5,6,7,3] => [7,6,4,3,2,1,5] => ? = 8
[1,2,4,5,7,3,6] => [7,6,4,3,1,5,2] => ? = 12
[1,2,4,5,7,6,3] => [7,6,4,3,1,2,5] => ? = 12
[1,2,4,6,3,5,7] => [7,6,4,2,5,3,1] => ? = 11
[1,2,4,6,3,7,5] => [7,6,4,2,5,1,3] => ? = 14
[1,2,4,6,5,3,7] => [7,6,4,2,3,5,1] => ? = 13
[1,2,4,6,5,7,3] => [7,6,4,2,3,1,5] => ? = 12
[1,2,4,6,7,3,5] => [7,6,4,2,1,5,3] => ? = 13
[1,2,4,6,7,5,3] => [7,6,4,2,1,3,5] => ? = 14
[1,2,4,7,3,5,6] => [7,6,4,1,5,3,2] => ? = 12
[1,2,4,7,3,6,5] => [7,6,4,1,5,2,3] => ? = 16
[1,2,4,7,5,3,6] => [7,6,4,1,3,5,2] => ? = 14
[1,2,4,7,5,6,3] => [7,6,4,1,3,2,5] => ? = 14
[1,2,4,7,6,3,5] => [7,6,4,1,2,5,3] => ? = 16
[1,2,4,7,6,5,3] => [7,6,4,1,2,3,5] => ? = 17
[1,2,5,3,4,6,7] => [7,6,3,5,4,2,1] => ? = 8
Description
The number of occurrences of the pattern 231 or of the pattern 312 in a permutation.