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Your data matches 4 different statistics following compositions of up to 3 maps.
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Matching statistic: St000100
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000100: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000100: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => [.,[.,.]]
=> [2,1] => ([],2)
=> 2
[2,1] => [[.,.],.]
=> [1,2] => ([(0,1)],2)
=> 1
[1,2,3] => [.,[.,[.,.]]]
=> [3,2,1] => ([],3)
=> 6
[1,3,2] => [.,[[.,.],.]]
=> [2,3,1] => ([(1,2)],3)
=> 3
[2,1,3] => [[.,.],[.,.]]
=> [1,3,2] => ([(0,1),(0,2)],3)
=> 2
[2,3,1] => [[.,.],[.,.]]
=> [1,3,2] => ([(0,1),(0,2)],3)
=> 2
[3,1,2] => [[.,[.,.]],.]
=> [2,1,3] => ([(0,2),(1,2)],3)
=> 2
[3,2,1] => [[[.,.],.],.]
=> [1,2,3] => ([(0,2),(2,1)],3)
=> 1
[1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [4,3,2,1] => ([],4)
=> 24
[1,2,4,3] => [.,[.,[[.,.],.]]]
=> [3,4,2,1] => ([(2,3)],4)
=> 12
[1,3,2,4] => [.,[[.,.],[.,.]]]
=> [2,4,3,1] => ([(1,2),(1,3)],4)
=> 8
[1,3,4,2] => [.,[[.,.],[.,.]]]
=> [2,4,3,1] => ([(1,2),(1,3)],4)
=> 8
[1,4,2,3] => [.,[[.,[.,.]],.]]
=> [3,2,4,1] => ([(1,3),(2,3)],4)
=> 8
[1,4,3,2] => [.,[[[.,.],.],.]]
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> 4
[2,1,3,4] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> 6
[2,1,4,3] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> 3
[2,3,1,4] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> 6
[2,3,4,1] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> 6
[2,4,1,3] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> 3
[2,4,3,1] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> 3
[3,1,2,4] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4
[3,1,4,2] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4
[3,2,1,4] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> 2
[3,2,4,1] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> 2
[3,4,1,2] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4
[3,4,2,1] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> 2
[4,1,2,3] => [[.,[.,[.,.]]],.]
=> [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> 6
[4,1,3,2] => [[.,[[.,.],.]],.]
=> [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> 3
[4,2,1,3] => [[[.,.],[.,.]],.]
=> [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[4,2,3,1] => [[[.,.],[.,.]],.]
=> [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[4,3,1,2] => [[[.,[.,.]],.],.]
=> [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> 2
[4,3,2,1] => [[[[.,.],.],.],.]
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [5,4,3,2,1] => ([],5)
=> 120
[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> [4,5,3,2,1] => ([(3,4)],5)
=> 60
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> [3,5,4,2,1] => ([(2,3),(2,4)],5)
=> 40
[1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]]
=> [3,5,4,2,1] => ([(2,3),(2,4)],5)
=> 40
[1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
=> [4,3,5,2,1] => ([(2,4),(3,4)],5)
=> 40
[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
=> [3,4,5,2,1] => ([(2,3),(3,4)],5)
=> 20
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> [2,5,4,3,1] => ([(1,2),(1,3),(1,4)],5)
=> 30
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> [2,4,5,3,1] => ([(1,3),(1,4),(4,2)],5)
=> 15
[1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]]
=> [2,5,4,3,1] => ([(1,2),(1,3),(1,4)],5)
=> 30
[1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
=> [2,5,4,3,1] => ([(1,2),(1,3),(1,4)],5)
=> 30
[1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [2,4,5,3,1] => ([(1,3),(1,4),(4,2)],5)
=> 15
[1,3,5,4,2] => [.,[[.,.],[[.,.],.]]]
=> [2,4,5,3,1] => ([(1,3),(1,4),(4,2)],5)
=> 15
[1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 20
[1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 20
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
=> [2,3,5,4,1] => ([(1,4),(4,2),(4,3)],5)
=> 10
[1,4,3,5,2] => [.,[[[.,.],.],[.,.]]]
=> [2,3,5,4,1] => ([(1,4),(4,2),(4,3)],5)
=> 10
[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5)
=> 20
[1,4,5,3,2] => [.,[[[.,.],.],[.,.]]]
=> [2,3,5,4,1] => ([(1,4),(4,2),(4,3)],5)
=> 10
Description
The number of linear extensions of a poset.
Matching statistic: St000110
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00018: Binary trees —left border symmetry⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
St000110: Permutations ⟶ ℤResult quality: 61% ●values known / values provided: 61%●distinct values known / distinct values provided: 97%
Mp00018: Binary trees —left border symmetry⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
St000110: Permutations ⟶ ℤResult quality: 61% ●values known / values provided: 61%●distinct values known / distinct values provided: 97%
Values
[1,2] => [.,[.,.]]
=> [.,[.,.]]
=> [2,1] => 2
[2,1] => [[.,.],.]
=> [[.,.],.]
=> [1,2] => 1
[1,2,3] => [.,[.,[.,.]]]
=> [.,[.,[.,.]]]
=> [3,2,1] => 6
[1,3,2] => [.,[[.,.],.]]
=> [.,[[.,.],.]]
=> [2,3,1] => 3
[2,1,3] => [[.,.],[.,.]]
=> [[.,[.,.]],.]
=> [2,1,3] => 2
[2,3,1] => [[.,.],[.,.]]
=> [[.,[.,.]],.]
=> [2,1,3] => 2
[3,1,2] => [[.,[.,.]],.]
=> [[.,.],[.,.]]
=> [1,3,2] => 2
[3,2,1] => [[[.,.],.],.]
=> [[[.,.],.],.]
=> [1,2,3] => 1
[1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [.,[.,[.,[.,.]]]]
=> [4,3,2,1] => 24
[1,2,4,3] => [.,[.,[[.,.],.]]]
=> [.,[.,[[.,.],.]]]
=> [3,4,2,1] => 12
[1,3,2,4] => [.,[[.,.],[.,.]]]
=> [.,[[.,[.,.]],.]]
=> [3,2,4,1] => 8
[1,3,4,2] => [.,[[.,.],[.,.]]]
=> [.,[[.,[.,.]],.]]
=> [3,2,4,1] => 8
[1,4,2,3] => [.,[[.,[.,.]],.]]
=> [.,[[.,.],[.,.]]]
=> [2,4,3,1] => 8
[1,4,3,2] => [.,[[[.,.],.],.]]
=> [.,[[[.,.],.],.]]
=> [2,3,4,1] => 4
[2,1,3,4] => [[.,.],[.,[.,.]]]
=> [[.,[.,[.,.]]],.]
=> [3,2,1,4] => 6
[2,1,4,3] => [[.,.],[[.,.],.]]
=> [[.,[[.,.],.]],.]
=> [2,3,1,4] => 3
[2,3,1,4] => [[.,.],[.,[.,.]]]
=> [[.,[.,[.,.]]],.]
=> [3,2,1,4] => 6
[2,3,4,1] => [[.,.],[.,[.,.]]]
=> [[.,[.,[.,.]]],.]
=> [3,2,1,4] => 6
[2,4,1,3] => [[.,.],[[.,.],.]]
=> [[.,[[.,.],.]],.]
=> [2,3,1,4] => 3
[2,4,3,1] => [[.,.],[[.,.],.]]
=> [[.,[[.,.],.]],.]
=> [2,3,1,4] => 3
[3,1,2,4] => [[.,[.,.]],[.,.]]
=> [[.,[.,.]],[.,.]]
=> [2,1,4,3] => 4
[3,1,4,2] => [[.,[.,.]],[.,.]]
=> [[.,[.,.]],[.,.]]
=> [2,1,4,3] => 4
[3,2,1,4] => [[[.,.],.],[.,.]]
=> [[[.,[.,.]],.],.]
=> [2,1,3,4] => 2
[3,2,4,1] => [[[.,.],.],[.,.]]
=> [[[.,[.,.]],.],.]
=> [2,1,3,4] => 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] => 6
[4,1,3,2] => [[.,[[.,.],.]],.]
=> [[.,.],[[.,.],.]]
=> [1,3,4,2] => 3
[4,2,1,3] => [[[.,.],[.,.]],.]
=> [[[.,.],[.,.]],.]
=> [1,3,2,4] => 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] => 1
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [.,[.,[.,[.,[.,.]]]]]
=> [5,4,3,2,1] => 120
[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> [.,[.,[.,[[.,.],.]]]]
=> [4,5,3,2,1] => 60
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> [.,[.,[[.,[.,.]],.]]]
=> [4,3,5,2,1] => 40
[1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]]
=> [.,[.,[[.,[.,.]],.]]]
=> [4,3,5,2,1] => 40
[1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
=> [.,[.,[[.,.],[.,.]]]]
=> [3,5,4,2,1] => 40
[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
=> [.,[.,[[[.,.],.],.]]]
=> [3,4,5,2,1] => 20
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> [.,[[.,[.,[.,.]]],.]]
=> [4,3,2,5,1] => 30
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> [.,[[.,[[.,.],.]],.]]
=> [3,4,2,5,1] => 15
[1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]]
=> [.,[[.,[.,[.,.]]],.]]
=> [4,3,2,5,1] => 30
[1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
=> [.,[[.,[.,[.,.]]],.]]
=> [4,3,2,5,1] => 30
[1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [.,[[.,[[.,.],.]],.]]
=> [3,4,2,5,1] => 15
[1,3,5,4,2] => [.,[[.,.],[[.,.],.]]]
=> [.,[[.,[[.,.],.]],.]]
=> [3,4,2,5,1] => 15
[1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]]
=> [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => 20
[1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => 20
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
=> [.,[[[.,[.,.]],.],.]]
=> [3,2,4,5,1] => 10
[1,4,3,5,2] => [.,[[[.,.],.],[.,.]]]
=> [.,[[[.,[.,.]],.],.]]
=> [3,2,4,5,1] => 10
[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => 20
[1,4,5,3,2] => [.,[[[.,.],.],[.,.]]]
=> [.,[[[.,[.,.]],.],.]]
=> [3,2,4,5,1] => 10
[2,1,3,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,1,3,6,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,1,3,6,7,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,1,3,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]]
=> [[.,[.,[[[[.,.],.],.],.]]],.]
=> [3,4,5,6,2,1,7] => ? = 30
[2,1,4,3,5,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
=> [[.,[[.,[.,[[.,.],.]]],.]],.]
=> [4,5,3,2,6,1,7] => ? = 72
[2,1,4,3,6,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
=> [[.,[[.,[[.,[.,.]],.]],.]],.]
=> [4,3,5,2,6,1,7] => ? = 48
[2,1,4,3,6,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
=> [[.,[[.,[[.,[.,.]],.]],.]],.]
=> [4,3,5,2,6,1,7] => ? = 48
[2,1,4,3,7,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
=> [[.,[[.,[[[.,.],.],.]],.]],.]
=> [3,4,5,2,6,1,7] => ? = 24
[2,1,4,5,3,7,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
=> [[.,[[.,[.,[[.,.],.]]],.]],.]
=> [4,5,3,2,6,1,7] => ? = 72
[2,1,4,5,7,3,6] => [[.,.],[[.,.],[.,[[.,.],.]]]]
=> [[.,[[.,[.,[[.,.],.]]],.]],.]
=> [4,5,3,2,6,1,7] => ? = 72
[2,1,4,5,7,6,3] => [[.,.],[[.,.],[.,[[.,.],.]]]]
=> [[.,[[.,[.,[[.,.],.]]],.]],.]
=> [4,5,3,2,6,1,7] => ? = 72
[2,1,4,6,3,5,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
=> [[.,[[.,[[.,[.,.]],.]],.]],.]
=> [4,3,5,2,6,1,7] => ? = 48
[2,1,4,6,3,7,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
=> [[.,[[.,[[.,[.,.]],.]],.]],.]
=> [4,3,5,2,6,1,7] => ? = 48
[2,1,4,6,5,3,7] => [[.,.],[[.,.],[[.,.],[.,.]]]]
=> [[.,[[.,[[.,[.,.]],.]],.]],.]
=> [4,3,5,2,6,1,7] => ? = 48
[2,1,4,6,5,7,3] => [[.,.],[[.,.],[[.,.],[.,.]]]]
=> [[.,[[.,[[.,[.,.]],.]],.]],.]
=> [4,3,5,2,6,1,7] => ? = 48
[2,1,4,6,7,3,5] => [[.,.],[[.,.],[[.,.],[.,.]]]]
=> [[.,[[.,[[.,[.,.]],.]],.]],.]
=> [4,3,5,2,6,1,7] => ? = 48
[2,1,4,6,7,5,3] => [[.,.],[[.,.],[[.,.],[.,.]]]]
=> [[.,[[.,[[.,[.,.]],.]],.]],.]
=> [4,3,5,2,6,1,7] => ? = 48
[2,1,4,7,3,6,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
=> [[.,[[.,[[[.,.],.],.]],.]],.]
=> [3,4,5,2,6,1,7] => ? = 24
[2,1,4,7,6,3,5] => [[.,.],[[.,.],[[[.,.],.],.]]]
=> [[.,[[.,[[[.,.],.],.]],.]],.]
=> [3,4,5,2,6,1,7] => ? = 24
[2,1,4,7,6,5,3] => [[.,.],[[.,.],[[[.,.],.],.]]]
=> [[.,[[.,[[[.,.],.],.]],.]],.]
=> [3,4,5,2,6,1,7] => ? = 24
[2,1,5,4,3,6,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
=> [[.,[[[.,[.,[.,.]]],.],.]],.]
=> [4,3,2,5,6,1,7] => ? = 36
[2,1,5,4,3,7,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
=> [[.,[[[.,[[.,.],.]],.],.]],.]
=> [3,4,2,5,6,1,7] => ? = 18
[2,1,5,4,6,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
=> [[.,[[[.,[.,[.,.]]],.],.]],.]
=> [4,3,2,5,6,1,7] => ? = 36
[2,1,5,4,6,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]]
=> [[.,[[[.,[.,[.,.]]],.],.]],.]
=> [4,3,2,5,6,1,7] => ? = 36
[2,1,5,4,7,3,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
=> [[.,[[[.,[[.,.],.]],.],.]],.]
=> [3,4,2,5,6,1,7] => ? = 18
[2,1,5,4,7,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]]
=> [[.,[[[.,[[.,.],.]],.],.]],.]
=> [3,4,2,5,6,1,7] => ? = 18
[2,1,5,6,4,3,7] => [[.,.],[[[.,.],.],[.,[.,.]]]]
=> [[.,[[[.,[.,[.,.]]],.],.]],.]
=> [4,3,2,5,6,1,7] => ? = 36
[2,1,5,6,4,7,3] => [[.,.],[[[.,.],.],[.,[.,.]]]]
=> [[.,[[[.,[.,[.,.]]],.],.]],.]
=> [4,3,2,5,6,1,7] => ? = 36
[2,1,5,6,7,4,3] => [[.,.],[[[.,.],.],[.,[.,.]]]]
=> [[.,[[[.,[.,[.,.]]],.],.]],.]
=> [4,3,2,5,6,1,7] => ? = 36
[2,1,5,7,4,3,6] => [[.,.],[[[.,.],.],[[.,.],.]]]
=> [[.,[[[.,[[.,.],.]],.],.]],.]
=> [3,4,2,5,6,1,7] => ? = 18
[2,1,5,7,4,6,3] => [[.,.],[[[.,.],.],[[.,.],.]]]
=> [[.,[[[.,[[.,.],.]],.],.]],.]
=> [3,4,2,5,6,1,7] => ? = 18
[2,1,5,7,6,4,3] => [[.,.],[[[.,.],.],[[.,.],.]]]
=> [[.,[[[.,[[.,.],.]],.],.]],.]
=> [3,4,2,5,6,1,7] => ? = 18
[2,1,6,5,4,3,7] => [[.,.],[[[[.,.],.],.],[.,.]]]
=> [[.,[[[[.,[.,.]],.],.],.]],.]
=> [3,2,4,5,6,1,7] => ? = 12
[2,1,6,5,4,7,3] => [[.,.],[[[[.,.],.],.],[.,.]]]
=> [[.,[[[[.,[.,.]],.],.],.]],.]
=> [3,2,4,5,6,1,7] => ? = 12
[2,1,6,5,7,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]]
=> [[.,[[[[.,[.,.]],.],.],.]],.]
=> [3,2,4,5,6,1,7] => ? = 12
[2,1,6,7,5,4,3] => [[.,.],[[[[.,.],.],.],[.,.]]]
=> [[.,[[[[.,[.,.]],.],.],.]],.]
=> [3,2,4,5,6,1,7] => ? = 12
[2,3,1,6,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,3,1,6,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,3,1,6,7,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,3,1,7,6,5,4] => [[.,.],[.,[[[[.,.],.],.],.]]]
=> [[.,[.,[[[[.,.],.],.],.]]],.]
=> [3,4,5,6,2,1,7] => ? = 30
[2,3,6,1,5,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,3,6,1,5,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,3,6,1,7,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,3,6,5,1,4,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,3,6,5,1,7,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,3,6,5,4,1,7] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,3,6,5,4,7,1] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,3,6,5,7,1,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,3,6,5,7,4,1] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
[2,3,6,7,1,5,4] => [[.,.],[.,[[[.,.],.],[.,.]]]]
=> [[.,[.,[[[.,[.,.]],.],.]]],.]
=> [4,3,5,6,2,1,7] => ? = 60
Description
The number of permutations less than or equal to a permutation in left weak order.
This is the same as the number of permutations less than or equal to the given permutation in right weak order.
Matching statistic: St001346
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Mp00064: Permutations —reverse⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
St001346: Permutations ⟶ ℤResult quality: 45% ●values known / values provided: 45%●distinct values known / distinct values provided: 78%
Mp00069: Permutations —complement⟶ Permutations
St001346: Permutations ⟶ ℤResult quality: 45% ●values known / values provided: 45%●distinct values known / distinct values provided: 78%
Values
[1,2] => [2,1] => [1,2] => 2
[2,1] => [1,2] => [2,1] => 1
[1,2,3] => [3,2,1] => [1,2,3] => 6
[1,3,2] => [2,3,1] => [2,1,3] => 3
[2,1,3] => [3,1,2] => [1,3,2] => 2
[2,3,1] => [1,3,2] => [3,1,2] => 2
[3,1,2] => [2,1,3] => [2,3,1] => 2
[3,2,1] => [1,2,3] => [3,2,1] => 1
[1,2,3,4] => [4,3,2,1] => [1,2,3,4] => 24
[1,2,4,3] => [3,4,2,1] => [2,1,3,4] => 12
[1,3,2,4] => [4,2,3,1] => [1,3,2,4] => 8
[1,3,4,2] => [2,4,3,1] => [3,1,2,4] => 8
[1,4,2,3] => [3,2,4,1] => [2,3,1,4] => 8
[1,4,3,2] => [2,3,4,1] => [3,2,1,4] => 4
[2,1,3,4] => [4,3,1,2] => [1,2,4,3] => 6
[2,1,4,3] => [3,4,1,2] => [2,1,4,3] => 3
[2,3,1,4] => [4,1,3,2] => [1,4,2,3] => 6
[2,3,4,1] => [1,4,3,2] => [4,1,2,3] => 6
[2,4,1,3] => [3,1,4,2] => [2,4,1,3] => 3
[2,4,3,1] => [1,3,4,2] => [4,2,1,3] => 3
[3,1,2,4] => [4,2,1,3] => [1,3,4,2] => 4
[3,1,4,2] => [2,4,1,3] => [3,1,4,2] => 4
[3,2,1,4] => [4,1,2,3] => [1,4,3,2] => 2
[3,2,4,1] => [1,4,2,3] => [4,1,3,2] => 2
[3,4,1,2] => [2,1,4,3] => [3,4,1,2] => 4
[3,4,2,1] => [1,2,4,3] => [4,3,1,2] => 2
[4,1,2,3] => [3,2,1,4] => [2,3,4,1] => 6
[4,1,3,2] => [2,3,1,4] => [3,2,4,1] => 3
[4,2,1,3] => [3,1,2,4] => [2,4,3,1] => 2
[4,2,3,1] => [1,3,2,4] => [4,2,3,1] => 2
[4,3,1,2] => [2,1,3,4] => [3,4,2,1] => 2
[4,3,2,1] => [1,2,3,4] => [4,3,2,1] => 1
[1,2,3,4,5] => [5,4,3,2,1] => [1,2,3,4,5] => 120
[1,2,3,5,4] => [4,5,3,2,1] => [2,1,3,4,5] => 60
[1,2,4,3,5] => [5,3,4,2,1] => [1,3,2,4,5] => 40
[1,2,4,5,3] => [3,5,4,2,1] => [3,1,2,4,5] => 40
[1,2,5,3,4] => [4,3,5,2,1] => [2,3,1,4,5] => 40
[1,2,5,4,3] => [3,4,5,2,1] => [3,2,1,4,5] => 20
[1,3,2,4,5] => [5,4,2,3,1] => [1,2,4,3,5] => 30
[1,3,2,5,4] => [4,5,2,3,1] => [2,1,4,3,5] => 15
[1,3,4,2,5] => [5,2,4,3,1] => [1,4,2,3,5] => 30
[1,3,4,5,2] => [2,5,4,3,1] => [4,1,2,3,5] => 30
[1,3,5,2,4] => [4,2,5,3,1] => [2,4,1,3,5] => 15
[1,3,5,4,2] => [2,4,5,3,1] => [4,2,1,3,5] => 15
[1,4,2,3,5] => [5,3,2,4,1] => [1,3,4,2,5] => 20
[1,4,2,5,3] => [3,5,2,4,1] => [3,1,4,2,5] => 20
[1,4,3,2,5] => [5,2,3,4,1] => [1,4,3,2,5] => 10
[1,4,3,5,2] => [2,5,3,4,1] => [4,1,3,2,5] => 10
[1,4,5,2,3] => [3,2,5,4,1] => [3,4,1,2,5] => 20
[1,4,5,3,2] => [2,3,5,4,1] => [4,3,1,2,5] => 10
[2,1,3,4,5,6,7] => [7,6,5,4,3,1,2] => [1,2,3,4,5,7,6] => ? = 720
[2,1,3,4,5,7,6] => [6,7,5,4,3,1,2] => [2,1,3,4,5,7,6] => ? = 360
[2,1,3,4,6,5,7] => [7,5,6,4,3,1,2] => [1,3,2,4,5,7,6] => ? = 240
[2,1,3,4,6,7,5] => [5,7,6,4,3,1,2] => [3,1,2,4,5,7,6] => ? = 240
[2,1,3,4,7,6,5] => [5,6,7,4,3,1,2] => [3,2,1,4,5,7,6] => ? = 120
[2,1,3,5,4,6,7] => [7,6,4,5,3,1,2] => [1,2,4,3,5,7,6] => ? = 180
[2,1,3,5,4,7,6] => [6,7,4,5,3,1,2] => [2,1,4,3,5,7,6] => ? = 90
[2,1,3,5,6,4,7] => [7,4,6,5,3,1,2] => [1,4,2,3,5,7,6] => ? = 180
[2,1,3,5,6,7,4] => [4,7,6,5,3,1,2] => [4,1,2,3,5,7,6] => ? = 180
[2,1,3,5,7,4,6] => [6,4,7,5,3,1,2] => [2,4,1,3,5,7,6] => ? = 90
[2,1,3,5,7,6,4] => [4,6,7,5,3,1,2] => [4,2,1,3,5,7,6] => ? = 90
[2,1,3,6,5,4,7] => [7,4,5,6,3,1,2] => [1,4,3,2,5,7,6] => ? = 60
[2,1,3,6,5,7,4] => [4,7,5,6,3,1,2] => [4,1,3,2,5,7,6] => ? = 60
[2,1,3,6,7,5,4] => [4,5,7,6,3,1,2] => [4,3,1,2,5,7,6] => ? = 60
[2,1,3,7,6,5,4] => [4,5,6,7,3,1,2] => [4,3,2,1,5,7,6] => ? = 30
[2,1,4,3,5,6,7] => [7,6,5,3,4,1,2] => [1,2,3,5,4,7,6] => ? = 144
[2,1,4,3,5,7,6] => [6,7,5,3,4,1,2] => [2,1,3,5,4,7,6] => ? = 72
[2,1,4,3,6,5,7] => [7,5,6,3,4,1,2] => [1,3,2,5,4,7,6] => ? = 48
[2,1,4,3,6,7,5] => [5,7,6,3,4,1,2] => [3,1,2,5,4,7,6] => ? = 48
[2,1,4,3,7,6,5] => [5,6,7,3,4,1,2] => [3,2,1,5,4,7,6] => ? = 24
[2,1,4,5,3,6,7] => [7,6,3,5,4,1,2] => [1,2,5,3,4,7,6] => ? = 144
[2,1,4,5,3,7,6] => [6,7,3,5,4,1,2] => [2,1,5,3,4,7,6] => ? = 72
[2,1,4,5,6,3,7] => [7,3,6,5,4,1,2] => [1,5,2,3,4,7,6] => ? = 144
[2,1,4,5,6,7,3] => [3,7,6,5,4,1,2] => [5,1,2,3,4,7,6] => ? = 144
[2,1,4,5,7,3,6] => [6,3,7,5,4,1,2] => [2,5,1,3,4,7,6] => ? = 72
[2,1,4,5,7,6,3] => [3,6,7,5,4,1,2] => [5,2,1,3,4,7,6] => ? = 72
[2,1,4,6,3,5,7] => [7,5,3,6,4,1,2] => [1,3,5,2,4,7,6] => ? = 48
[2,1,4,6,3,7,5] => [5,7,3,6,4,1,2] => [3,1,5,2,4,7,6] => ? = 48
[2,1,4,6,5,3,7] => [7,3,5,6,4,1,2] => [1,5,3,2,4,7,6] => ? = 48
[2,1,4,6,5,7,3] => [3,7,5,6,4,1,2] => [5,1,3,2,4,7,6] => ? = 48
[2,1,4,6,7,3,5] => [5,3,7,6,4,1,2] => [3,5,1,2,4,7,6] => ? = 48
[2,1,4,6,7,5,3] => [3,5,7,6,4,1,2] => [5,3,1,2,4,7,6] => ? = 48
[2,1,4,7,3,6,5] => [5,6,3,7,4,1,2] => [3,2,5,1,4,7,6] => ? = 24
[2,1,4,7,6,3,5] => [5,3,6,7,4,1,2] => [3,5,2,1,4,7,6] => ? = 24
[2,1,4,7,6,5,3] => [3,5,6,7,4,1,2] => [5,3,2,1,4,7,6] => ? = 24
[2,1,5,4,3,6,7] => [7,6,3,4,5,1,2] => [1,2,5,4,3,7,6] => ? = 36
[2,1,5,4,3,7,6] => [6,7,3,4,5,1,2] => [2,1,5,4,3,7,6] => ? = 18
[2,1,5,4,6,3,7] => [7,3,6,4,5,1,2] => [1,5,2,4,3,7,6] => ? = 36
[2,1,5,4,6,7,3] => [3,7,6,4,5,1,2] => [5,1,2,4,3,7,6] => ? = 36
[2,1,5,4,7,3,6] => [6,3,7,4,5,1,2] => [2,5,1,4,3,7,6] => ? = 18
[2,1,5,4,7,6,3] => [3,6,7,4,5,1,2] => [5,2,1,4,3,7,6] => ? = 18
[2,1,5,6,4,3,7] => [7,3,4,6,5,1,2] => [1,5,4,2,3,7,6] => ? = 36
[2,1,5,6,4,7,3] => [3,7,4,6,5,1,2] => [5,1,4,2,3,7,6] => ? = 36
[2,1,5,6,7,4,3] => [3,4,7,6,5,1,2] => [5,4,1,2,3,7,6] => ? = 36
[2,1,5,7,4,3,6] => [6,3,4,7,5,1,2] => [2,5,4,1,3,7,6] => ? = 18
[2,1,5,7,4,6,3] => [3,6,4,7,5,1,2] => [5,2,4,1,3,7,6] => ? = 18
[2,1,5,7,6,4,3] => [3,4,6,7,5,1,2] => [5,4,2,1,3,7,6] => ? = 18
[2,1,6,5,4,3,7] => [7,3,4,5,6,1,2] => [1,5,4,3,2,7,6] => ? = 12
[2,1,6,5,4,7,3] => [3,7,4,5,6,1,2] => [5,1,4,3,2,7,6] => ? = 12
[2,1,6,5,7,4,3] => [3,4,7,5,6,1,2] => [5,4,1,3,2,7,6] => ? = 12
Description
The number of parking functions that give the same permutation.
A '''parking function''' $(a_1,\dots,a_n)$ is a list of preferred parking spots of $n$ cars entering a one-way street. Once the cars have parked, the order of the cars gives a permutation of $\{1,\dots,n\}$. This statistic records the number of parking functions that yield the same permutation of cars.
Matching statistic: St001855
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001855: Signed permutations ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 22%
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001855: Signed permutations ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 22%
Values
[1,2] => [.,[.,.]]
=> [2,1] => [2,1] => 2
[2,1] => [[.,.],.]
=> [1,2] => [1,2] => 1
[1,2,3] => [.,[.,[.,.]]]
=> [3,2,1] => [3,2,1] => 6
[1,3,2] => [.,[[.,.],.]]
=> [2,3,1] => [2,3,1] => 3
[2,1,3] => [[.,.],[.,.]]
=> [1,3,2] => [1,3,2] => 2
[2,3,1] => [[.,.],[.,.]]
=> [1,3,2] => [1,3,2] => 2
[3,1,2] => [[.,[.,.]],.]
=> [2,1,3] => [2,1,3] => 2
[3,2,1] => [[[.,.],.],.]
=> [1,2,3] => [1,2,3] => 1
[1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [4,3,2,1] => [4,3,2,1] => 24
[1,2,4,3] => [.,[.,[[.,.],.]]]
=> [3,4,2,1] => [3,4,2,1] => 12
[1,3,2,4] => [.,[[.,.],[.,.]]]
=> [2,4,3,1] => [2,4,3,1] => 8
[1,3,4,2] => [.,[[.,.],[.,.]]]
=> [2,4,3,1] => [2,4,3,1] => 8
[1,4,2,3] => [.,[[.,[.,.]],.]]
=> [3,2,4,1] => [3,2,4,1] => 8
[1,4,3,2] => [.,[[[.,.],.],.]]
=> [2,3,4,1] => [2,3,4,1] => 4
[2,1,3,4] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => [1,4,3,2] => 6
[2,1,4,3] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => [1,3,4,2] => 3
[2,3,1,4] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => [1,4,3,2] => 6
[2,3,4,1] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => [1,4,3,2] => 6
[2,4,1,3] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => [1,3,4,2] => 3
[2,4,3,1] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => [1,3,4,2] => 3
[3,1,2,4] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => [2,1,4,3] => 4
[3,1,4,2] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => [2,1,4,3] => 4
[3,2,1,4] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => [1,2,4,3] => 2
[3,2,4,1] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => [1,2,4,3] => 2
[3,4,1,2] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => [2,1,4,3] => 4
[3,4,2,1] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => [1,2,4,3] => 2
[4,1,2,3] => [[.,[.,[.,.]]],.]
=> [3,2,1,4] => [3,2,1,4] => 6
[4,1,3,2] => [[.,[[.,.],.]],.]
=> [2,3,1,4] => [2,3,1,4] => 3
[4,2,1,3] => [[[.,.],[.,.]],.]
=> [1,3,2,4] => [1,3,2,4] => 2
[4,2,3,1] => [[[.,.],[.,.]],.]
=> [1,3,2,4] => [1,3,2,4] => 2
[4,3,1,2] => [[[.,[.,.]],.],.]
=> [2,1,3,4] => [2,1,3,4] => 2
[4,3,2,1] => [[[[.,.],.],.],.]
=> [1,2,3,4] => [1,2,3,4] => 1
[1,2,3,4,5] => [.,[.,[.,[.,[.,.]]]]]
=> [5,4,3,2,1] => [5,4,3,2,1] => ? = 120
[1,2,3,5,4] => [.,[.,[.,[[.,.],.]]]]
=> [4,5,3,2,1] => [4,5,3,2,1] => ? = 60
[1,2,4,3,5] => [.,[.,[[.,.],[.,.]]]]
=> [3,5,4,2,1] => [3,5,4,2,1] => ? = 40
[1,2,4,5,3] => [.,[.,[[.,.],[.,.]]]]
=> [3,5,4,2,1] => [3,5,4,2,1] => ? = 40
[1,2,5,3,4] => [.,[.,[[.,[.,.]],.]]]
=> [4,3,5,2,1] => [4,3,5,2,1] => ? = 40
[1,2,5,4,3] => [.,[.,[[[.,.],.],.]]]
=> [3,4,5,2,1] => [3,4,5,2,1] => ? = 20
[1,3,2,4,5] => [.,[[.,.],[.,[.,.]]]]
=> [2,5,4,3,1] => [2,5,4,3,1] => ? = 30
[1,3,2,5,4] => [.,[[.,.],[[.,.],.]]]
=> [2,4,5,3,1] => [2,4,5,3,1] => ? = 15
[1,3,4,2,5] => [.,[[.,.],[.,[.,.]]]]
=> [2,5,4,3,1] => [2,5,4,3,1] => ? = 30
[1,3,4,5,2] => [.,[[.,.],[.,[.,.]]]]
=> [2,5,4,3,1] => [2,5,4,3,1] => ? = 30
[1,3,5,2,4] => [.,[[.,.],[[.,.],.]]]
=> [2,4,5,3,1] => [2,4,5,3,1] => ? = 15
[1,3,5,4,2] => [.,[[.,.],[[.,.],.]]]
=> [2,4,5,3,1] => [2,4,5,3,1] => ? = 15
[1,4,2,3,5] => [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => [3,2,5,4,1] => ? = 20
[1,4,2,5,3] => [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => [3,2,5,4,1] => ? = 20
[1,4,3,2,5] => [.,[[[.,.],.],[.,.]]]
=> [2,3,5,4,1] => [2,3,5,4,1] => ? = 10
[1,4,3,5,2] => [.,[[[.,.],.],[.,.]]]
=> [2,3,5,4,1] => [2,3,5,4,1] => ? = 10
[1,4,5,2,3] => [.,[[.,[.,.]],[.,.]]]
=> [3,2,5,4,1] => [3,2,5,4,1] => ? = 20
[1,4,5,3,2] => [.,[[[.,.],.],[.,.]]]
=> [2,3,5,4,1] => [2,3,5,4,1] => ? = 10
[1,5,2,3,4] => [.,[[.,[.,[.,.]]],.]]
=> [4,3,2,5,1] => [4,3,2,5,1] => ? = 30
[1,5,2,4,3] => [.,[[.,[[.,.],.]],.]]
=> [3,4,2,5,1] => [3,4,2,5,1] => ? = 15
[1,5,3,2,4] => [.,[[[.,.],[.,.]],.]]
=> [2,4,3,5,1] => [2,4,3,5,1] => ? = 10
[1,5,3,4,2] => [.,[[[.,.],[.,.]],.]]
=> [2,4,3,5,1] => [2,4,3,5,1] => ? = 10
[1,5,4,2,3] => [.,[[[.,[.,.]],.],.]]
=> [3,2,4,5,1] => [3,2,4,5,1] => ? = 10
[1,5,4,3,2] => [.,[[[[.,.],.],.],.]]
=> [2,3,4,5,1] => [2,3,4,5,1] => ? = 5
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
=> [1,5,4,3,2] => [1,5,4,3,2] => 24
[2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
=> [1,4,5,3,2] => [1,4,5,3,2] => 12
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => [1,3,5,4,2] => 8
[2,1,4,5,3] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => [1,3,5,4,2] => 8
[2,1,5,3,4] => [[.,.],[[.,[.,.]],.]]
=> [1,4,3,5,2] => [1,4,3,5,2] => 8
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
=> [1,3,4,5,2] => [1,3,4,5,2] => 4
[2,3,1,4,5] => [[.,.],[.,[.,[.,.]]]]
=> [1,5,4,3,2] => [1,5,4,3,2] => 24
[2,3,1,5,4] => [[.,.],[.,[[.,.],.]]]
=> [1,4,5,3,2] => [1,4,5,3,2] => 12
[2,3,4,1,5] => [[.,.],[.,[.,[.,.]]]]
=> [1,5,4,3,2] => [1,5,4,3,2] => 24
[2,3,4,5,1] => [[.,.],[.,[.,[.,.]]]]
=> [1,5,4,3,2] => [1,5,4,3,2] => 24
[2,3,5,1,4] => [[.,.],[.,[[.,.],.]]]
=> [1,4,5,3,2] => [1,4,5,3,2] => 12
[2,3,5,4,1] => [[.,.],[.,[[.,.],.]]]
=> [1,4,5,3,2] => [1,4,5,3,2] => 12
[2,4,1,3,5] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => [1,3,5,4,2] => 8
[2,4,1,5,3] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => [1,3,5,4,2] => 8
[2,4,3,1,5] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => [1,3,5,4,2] => 8
[2,4,3,5,1] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => [1,3,5,4,2] => 8
[2,4,5,1,3] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => [1,3,5,4,2] => 8
[2,4,5,3,1] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => [1,3,5,4,2] => 8
[3,1,2,4,5] => [[.,[.,.]],[.,[.,.]]]
=> [2,1,5,4,3] => [2,1,5,4,3] => ? = 12
[3,1,2,5,4] => [[.,[.,.]],[[.,.],.]]
=> [2,1,4,5,3] => [2,1,4,5,3] => ? = 6
[3,1,4,2,5] => [[.,[.,.]],[.,[.,.]]]
=> [2,1,5,4,3] => [2,1,5,4,3] => ? = 12
[3,1,4,5,2] => [[.,[.,.]],[.,[.,.]]]
=> [2,1,5,4,3] => [2,1,5,4,3] => ? = 12
[3,1,5,2,4] => [[.,[.,.]],[[.,.],.]]
=> [2,1,4,5,3] => [2,1,4,5,3] => ? = 6
[3,1,5,4,2] => [[.,[.,.]],[[.,.],.]]
=> [2,1,4,5,3] => [2,1,4,5,3] => ? = 6
[3,4,1,2,5] => [[.,[.,.]],[.,[.,.]]]
=> [2,1,5,4,3] => [2,1,5,4,3] => ? = 12
[3,4,1,5,2] => [[.,[.,.]],[.,[.,.]]]
=> [2,1,5,4,3] => [2,1,5,4,3] => ? = 12
[3,4,5,1,2] => [[.,[.,.]],[.,[.,.]]]
=> [2,1,5,4,3] => [2,1,5,4,3] => ? = 12
[3,5,1,2,4] => [[.,[.,.]],[[.,.],.]]
=> [2,1,4,5,3] => [2,1,4,5,3] => ? = 6
[3,5,1,4,2] => [[.,[.,.]],[[.,.],.]]
=> [2,1,4,5,3] => [2,1,4,5,3] => ? = 6
[3,5,4,1,2] => [[.,[.,.]],[[.,.],.]]
=> [2,1,4,5,3] => [2,1,4,5,3] => ? = 6
[4,1,2,3,5] => [[.,[.,[.,.]]],[.,.]]
=> [3,2,1,5,4] => [3,2,1,5,4] => ? = 12
[4,1,2,5,3] => [[.,[.,[.,.]]],[.,.]]
=> [3,2,1,5,4] => [3,2,1,5,4] => ? = 12
[4,1,3,2,5] => [[.,[[.,.],.]],[.,.]]
=> [2,3,1,5,4] => [2,3,1,5,4] => ? = 6
[4,1,3,5,2] => [[.,[[.,.],.]],[.,.]]
=> [2,3,1,5,4] => [2,3,1,5,4] => ? = 6
[4,1,5,2,3] => [[.,[.,[.,.]]],[.,.]]
=> [3,2,1,5,4] => [3,2,1,5,4] => ? = 12
[4,1,5,3,2] => [[.,[[.,.],.]],[.,.]]
=> [2,3,1,5,4] => [2,3,1,5,4] => ? = 6
[4,3,1,2,5] => [[[.,[.,.]],.],[.,.]]
=> [2,1,3,5,4] => [2,1,3,5,4] => ? = 4
[4,3,1,5,2] => [[[.,[.,.]],.],[.,.]]
=> [2,1,3,5,4] => [2,1,3,5,4] => ? = 4
[4,3,5,1,2] => [[[.,[.,.]],.],[.,.]]
=> [2,1,3,5,4] => [2,1,3,5,4] => ? = 4
[4,5,1,2,3] => [[.,[.,[.,.]]],[.,.]]
=> [3,2,1,5,4] => [3,2,1,5,4] => ? = 12
[4,5,1,3,2] => [[.,[[.,.],.]],[.,.]]
=> [2,3,1,5,4] => [2,3,1,5,4] => ? = 6
[4,5,3,1,2] => [[[.,[.,.]],.],[.,.]]
=> [2,1,3,5,4] => [2,1,3,5,4] => ? = 4
[5,1,2,3,4] => [[.,[.,[.,[.,.]]]],.]
=> [4,3,2,1,5] => [4,3,2,1,5] => ? = 24
[5,1,2,4,3] => [[.,[.,[[.,.],.]]],.]
=> [3,4,2,1,5] => [3,4,2,1,5] => ? = 12
Description
The number of signed permutations less than or equal to a signed permutation in left weak order.
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