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Your data matches 5 different statistics following compositions of up to 3 maps.
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Matching statistic: St000218
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
St000218: 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] => 0
[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] => 0
[1,3,2,4] => 1
[1,3,4,2] => 0
[1,4,2,3] => 0
[1,4,3,2] => 0
[2,1,3,4] => 2
[2,1,4,3] => 2
[2,3,1,4] => 2
[2,3,4,1] => 0
[2,4,1,3] => 1
[2,4,3,1] => 0
[3,1,2,4] => 2
[3,1,4,2] => 1
[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] => 0
[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] => 0
[1,2,4,3,5] => 1
[1,2,4,5,3] => 0
[1,2,5,3,4] => 0
[1,2,5,4,3] => 0
[1,3,2,4,5] => 2
[1,3,2,5,4] => 2
[1,3,4,2,5] => 2
[1,3,4,5,2] => 0
[1,3,5,2,4] => 1
[1,3,5,4,2] => 0
[1,4,2,3,5] => 2
[1,4,2,5,3] => 1
[1,4,3,2,5] => 3
[1,4,3,5,2] => 1
[1,4,5,2,3] => 0
Description
The number of occurrences of the pattern 213 in a permutation.
Matching statistic: St000217
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00064: Permutations —reverse⟶ Permutations
St000217: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000217: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => 0
[1,2] => [2,1] => 0
[2,1] => [1,2] => 0
[1,2,3] => [3,2,1] => 0
[1,3,2] => [2,3,1] => 0
[2,1,3] => [3,1,2] => 1
[2,3,1] => [1,3,2] => 0
[3,1,2] => [2,1,3] => 0
[3,2,1] => [1,2,3] => 0
[1,2,3,4] => [4,3,2,1] => 0
[1,2,4,3] => [3,4,2,1] => 0
[1,3,2,4] => [4,2,3,1] => 1
[1,3,4,2] => [2,4,3,1] => 0
[1,4,2,3] => [3,2,4,1] => 0
[1,4,3,2] => [2,3,4,1] => 0
[2,1,3,4] => [4,3,1,2] => 2
[2,1,4,3] => [3,4,1,2] => 2
[2,3,1,4] => [4,1,3,2] => 2
[2,3,4,1] => [1,4,3,2] => 0
[2,4,1,3] => [3,1,4,2] => 1
[2,4,3,1] => [1,3,4,2] => 0
[3,1,2,4] => [4,2,1,3] => 2
[3,1,4,2] => [2,4,1,3] => 1
[3,2,1,4] => [4,1,2,3] => 3
[3,2,4,1] => [1,4,2,3] => 1
[3,4,1,2] => [2,1,4,3] => 0
[3,4,2,1] => [1,2,4,3] => 0
[4,1,2,3] => [3,2,1,4] => 0
[4,1,3,2] => [2,3,1,4] => 0
[4,2,1,3] => [3,1,2,4] => 1
[4,2,3,1] => [1,3,2,4] => 0
[4,3,1,2] => [2,1,3,4] => 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] => [4,5,3,2,1] => 0
[1,2,4,3,5] => [5,3,4,2,1] => 1
[1,2,4,5,3] => [3,5,4,2,1] => 0
[1,2,5,3,4] => [4,3,5,2,1] => 0
[1,2,5,4,3] => [3,4,5,2,1] => 0
[1,3,2,4,5] => [5,4,2,3,1] => 2
[1,3,2,5,4] => [4,5,2,3,1] => 2
[1,3,4,2,5] => [5,2,4,3,1] => 2
[1,3,4,5,2] => [2,5,4,3,1] => 0
[1,3,5,2,4] => [4,2,5,3,1] => 1
[1,3,5,4,2] => [2,4,5,3,1] => 0
[1,4,2,3,5] => [5,3,2,4,1] => 2
[1,4,2,5,3] => [3,5,2,4,1] => 1
[1,4,3,2,5] => [5,2,3,4,1] => 3
[1,4,3,5,2] => [2,5,3,4,1] => 1
[1,4,5,2,3] => [3,2,5,4,1] => 0
Description
The number of occurrences of the pattern 312 in a permutation.
Matching statistic: St000220
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00064: Permutations —reverse⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
St000220: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00069: Permutations —complement⟶ Permutations
St000220: Permutations ⟶ 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
[2,1] => [1,2] => [2,1] => 0
[1,2,3] => [3,2,1] => [1,2,3] => 0
[1,3,2] => [2,3,1] => [2,1,3] => 0
[2,1,3] => [3,1,2] => [1,3,2] => 1
[2,3,1] => [1,3,2] => [3,1,2] => 0
[3,1,2] => [2,1,3] => [2,3,1] => 0
[3,2,1] => [1,2,3] => [3,2,1] => 0
[1,2,3,4] => [4,3,2,1] => [1,2,3,4] => 0
[1,2,4,3] => [3,4,2,1] => [2,1,3,4] => 0
[1,3,2,4] => [4,2,3,1] => [1,3,2,4] => 1
[1,3,4,2] => [2,4,3,1] => [3,1,2,4] => 0
[1,4,2,3] => [3,2,4,1] => [2,3,1,4] => 0
[1,4,3,2] => [2,3,4,1] => [3,2,1,4] => 0
[2,1,3,4] => [4,3,1,2] => [1,2,4,3] => 2
[2,1,4,3] => [3,4,1,2] => [2,1,4,3] => 2
[2,3,1,4] => [4,1,3,2] => [1,4,2,3] => 2
[2,3,4,1] => [1,4,3,2] => [4,1,2,3] => 0
[2,4,1,3] => [3,1,4,2] => [2,4,1,3] => 1
[2,4,3,1] => [1,3,4,2] => [4,2,1,3] => 0
[3,1,2,4] => [4,2,1,3] => [1,3,4,2] => 2
[3,1,4,2] => [2,4,1,3] => [3,1,4,2] => 1
[3,2,1,4] => [4,1,2,3] => [1,4,3,2] => 3
[3,2,4,1] => [1,4,2,3] => [4,1,3,2] => 1
[3,4,1,2] => [2,1,4,3] => [3,4,1,2] => 0
[3,4,2,1] => [1,2,4,3] => [4,3,1,2] => 0
[4,1,2,3] => [3,2,1,4] => [2,3,4,1] => 0
[4,1,3,2] => [2,3,1,4] => [3,2,4,1] => 0
[4,2,1,3] => [3,1,2,4] => [2,4,3,1] => 1
[4,2,3,1] => [1,3,2,4] => [4,2,3,1] => 0
[4,3,1,2] => [2,1,3,4] => [3,4,2,1] => 0
[4,3,2,1] => [1,2,3,4] => [4,3,2,1] => 0
[1,2,3,4,5] => [5,4,3,2,1] => [1,2,3,4,5] => 0
[1,2,3,5,4] => [4,5,3,2,1] => [2,1,3,4,5] => 0
[1,2,4,3,5] => [5,3,4,2,1] => [1,3,2,4,5] => 1
[1,2,4,5,3] => [3,5,4,2,1] => [3,1,2,4,5] => 0
[1,2,5,3,4] => [4,3,5,2,1] => [2,3,1,4,5] => 0
[1,2,5,4,3] => [3,4,5,2,1] => [3,2,1,4,5] => 0
[1,3,2,4,5] => [5,4,2,3,1] => [1,2,4,3,5] => 2
[1,3,2,5,4] => [4,5,2,3,1] => [2,1,4,3,5] => 2
[1,3,4,2,5] => [5,2,4,3,1] => [1,4,2,3,5] => 2
[1,3,4,5,2] => [2,5,4,3,1] => [4,1,2,3,5] => 0
[1,3,5,2,4] => [4,2,5,3,1] => [2,4,1,3,5] => 1
[1,3,5,4,2] => [2,4,5,3,1] => [4,2,1,3,5] => 0
[1,4,2,3,5] => [5,3,2,4,1] => [1,3,4,2,5] => 2
[1,4,2,5,3] => [3,5,2,4,1] => [3,1,4,2,5] => 1
[1,4,3,2,5] => [5,2,3,4,1] => [1,4,3,2,5] => 3
[1,4,3,5,2] => [2,5,3,4,1] => [4,1,3,2,5] => 1
[1,4,5,2,3] => [3,2,5,4,1] => [3,4,1,2,5] => 0
Description
The number of occurrences of the pattern 132 in a permutation.
Matching statistic: St001398
Values
[1] => ([],1)
=> ([],1)
=> 0
[1,2] => ([(0,1)],2)
=> ([(0,1)],2)
=> 0
[2,1] => ([],2)
=> ([],2)
=> 0
[1,2,3] => ([(0,2),(2,1)],3)
=> ([(0,2),(2,1)],3)
=> 0
[1,3,2] => ([(0,1),(0,2)],3)
=> ([(0,2),(1,2)],3)
=> 0
[2,1,3] => ([(0,2),(1,2)],3)
=> ([(0,1),(0,2)],3)
=> 1
[2,3,1] => ([(1,2)],3)
=> ([(1,2)],3)
=> 0
[3,1,2] => ([(1,2)],3)
=> ([(1,2)],3)
=> 0
[3,2,1] => ([],3)
=> ([],3)
=> 0
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> ([(0,3),(2,1),(3,2)],4)
=> 0
[1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> ([(0,3),(1,3),(3,2)],4)
=> 0
[1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 1
[1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 0
[1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> 0
[1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> ([(0,3),(1,3),(2,3)],4)
=> 0
[2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> ([(0,3),(3,1),(3,2)],4)
=> 2
[2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> 2
[2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(0,3),(3,1)],4)
=> 2
[2,3,4,1] => ([(1,2),(2,3)],4)
=> ([(1,2),(2,3)],4)
=> 0
[2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2),(1,3)],4)
=> 1
[2,4,3,1] => ([(1,2),(1,3)],4)
=> ([(1,3),(2,3)],4)
=> 0
[3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,2),(0,3),(3,1)],4)
=> 2
[3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
=> ([(0,3),(1,2),(1,3)],4)
=> 1
[3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3)],4)
=> 3
[3,2,4,1] => ([(1,3),(2,3)],4)
=> ([(1,2),(1,3)],4)
=> 1
[3,4,1,2] => ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> 0
[3,4,2,1] => ([(2,3)],4)
=> ([(2,3)],4)
=> 0
[4,1,2,3] => ([(1,2),(2,3)],4)
=> ([(1,2),(2,3)],4)
=> 0
[4,1,3,2] => ([(1,2),(1,3)],4)
=> ([(1,3),(2,3)],4)
=> 0
[4,2,1,3] => ([(1,3),(2,3)],4)
=> ([(1,2),(1,3)],4)
=> 1
[4,2,3,1] => ([(2,3)],4)
=> ([(2,3)],4)
=> 0
[4,3,1,2] => ([(2,3)],4)
=> ([(2,3)],4)
=> 0
[4,3,2,1] => ([],4)
=> ([],4)
=> 0
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
[1,2,3,5,4] => ([(0,3),(3,4),(4,1),(4,2)],5)
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> 0
[1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> 1
[1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> 0
[1,2,5,3,4] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> 0
[1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
=> ([(0,4),(1,4),(2,4),(4,3)],5)
=> 0
[1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
=> ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
=> 2
[1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> ([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)
=> 2
[1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 2
[1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> 0
[1,3,5,2,4] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> 1
[1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> 0
[1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 2
[1,4,2,5,3] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
=> ([(0,3),(1,2),(1,3),(2,4),(3,4)],5)
=> 1
[1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 3
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
=> 1
[1,4,5,2,3] => ([(0,3),(0,4),(3,2),(4,1)],5)
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> 0
[] => ([],0)
=> ([],0)
=> ? = 0
Description
Number of subsets of size 3 of elements in a poset that form a "v".
For a finite poset (P,≤), this is the number of sets \{x,y,z\} \in \binom{P}{3} that form a "v"-subposet (i.e., a subposet consisting of a bottom element covered by two incomparable elements).
Matching statistic: St000219
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00069: Permutations —complement⟶ Permutations
St000219: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
St000219: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
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] => 0
[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] => 0
[1,3,2,4] => [4,2,3,1] => 1
[1,3,4,2] => [4,2,1,3] => 0
[1,4,2,3] => [4,1,3,2] => 0
[1,4,3,2] => [4,1,2,3] => 0
[2,1,3,4] => [3,4,2,1] => 2
[2,1,4,3] => [3,4,1,2] => 2
[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] => 1
[2,4,3,1] => [3,1,2,4] => 0
[3,1,2,4] => [2,4,3,1] => 2
[3,1,4,2] => [2,4,1,3] => 1
[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] => 0
[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] => 0
[1,2,4,3,5] => [5,4,2,3,1] => 1
[1,2,4,5,3] => [5,4,2,1,3] => 0
[1,2,5,3,4] => [5,4,1,3,2] => 0
[1,2,5,4,3] => [5,4,1,2,3] => 0
[1,3,2,4,5] => [5,3,4,2,1] => 2
[1,3,2,5,4] => [5,3,4,1,2] => 2
[1,3,4,2,5] => [5,3,2,4,1] => 2
[1,3,4,5,2] => [5,3,2,1,4] => 0
[1,3,5,2,4] => [5,3,1,4,2] => 1
[1,3,5,4,2] => [5,3,1,2,4] => 0
[1,4,2,3,5] => [5,2,4,3,1] => 2
[1,4,2,5,3] => [5,2,4,1,3] => 1
[1,4,3,2,5] => [5,2,3,4,1] => 3
[1,4,3,5,2] => [5,2,3,1,4] => 1
[1,4,5,2,3] => [5,2,1,4,3] => 0
[1,4,5,3,2] => [5,2,1,3,4] => 0
[1,5,2,3,4] => [5,1,4,3,2] => 0
[1,5,2,4,3] => [5,1,4,2,3] => 0
[] => [] => ? = 0
Description
The number of occurrences of the pattern 231 in a permutation.
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