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