searching the database
Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000110
(load all 4 compositions to match this statistic)
(load all 4 compositions to match this statistic)
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
St000110: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
St000110: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [.,.]
=> [1] => 1
[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] => [[.,.],[.,.]]
=> [1,3,2] => 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] => [.,[[.,.],[.,.]]]
=> [2,4,3,1] => 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] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => 6
[2,1,4,3] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => 3
[2,3,1,4] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => 4
[2,3,4,1] => [[.,[.,[.,.]]],.]
=> [3,2,1,4] => 6
[2,4,1,3] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => 4
[2,4,3,1] => [[.,[[.,.],.]],.]
=> [2,3,1,4] => 3
[3,1,2,4] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => 6
[3,1,4,2] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => 3
[3,2,1,4] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => 2
[3,2,4,1] => [[[.,.],[.,.]],.]
=> [1,3,2,4] => 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] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => 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
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
=> [1,5,4,3,2] => 24
[2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
=> [1,4,5,3,2] => 12
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => 8
[2,1,4,5,3] => [[.,.],[[.,[.,.]],.]]
=> [1,4,3,5,2] => 8
[2,1,5,3,4] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => 8
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
=> [1,3,4,5,2] => 4
[3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]]
=> [1,5,4,3,2] => 24
[3,1,2,5,4] => [[.,.],[.,[[.,.],.]]]
=> [1,4,5,3,2] => 12
[3,1,4,2,5] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => 8
[3,1,4,5,2] => [[.,.],[[.,[.,.]],.]]
=> [1,4,3,5,2] => 8
[3,1,5,2,4] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => 8
[3,1,5,4,2] => [[.,.],[[[.,.],.],.]]
=> [1,3,4,5,2] => 4
[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
=> [1,2,5,4,3] => 6
[3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
=> [1,2,4,5,3] => 3
[3,2,4,1,5] => [[[.,.],[.,.]],[.,.]]
=> [1,3,2,5,4] => 4
[3,2,4,5,1] => [[[.,.],[.,[.,.]]],.]
=> [1,4,3,2,5] => 6
[3,2,5,1,4] => [[[.,.],[.,.]],[.,.]]
=> [1,3,2,5,4] => 4
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: St001855
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001855: Signed permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001855: Signed permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [.,.]
=> [1] => [1] => 1
[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] => [[.,[.,.]],.]
=> [2,1,3] => [2,1,3] => 2
[3,1,2] => [[.,.],[.,.]]
=> [1,3,2] => [1,3,2] => 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] => [.,[[.,[.,.]],.]]
=> [3,2,4,1] => [3,2,4,1] => 8
[1,4,2,3] => [.,[[.,.],[.,.]]]
=> [2,4,3,1] => [2,4,3,1] => 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] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => [2,1,4,3] => 4
[2,3,4,1] => [[.,[.,[.,.]]],.]
=> [3,2,1,4] => [3,2,1,4] => 6
[2,4,1,3] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => [2,1,4,3] => 4
[2,4,3,1] => [[.,[[.,.],.]],.]
=> [2,3,1,4] => [2,3,1,4] => 3
[3,1,2,4] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => [1,4,3,2] => 6
[3,1,4,2] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => [1,3,4,2] => 3
[3,2,1,4] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => [1,2,4,3] => 2
[3,2,4,1] => [[[.,.],[.,.]],.]
=> [1,3,2,4] => [1,3,2,4] => 2
[3,4,1,2] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => [2,1,4,3] => 4
[3,4,2,1] => [[[.,[.,.]],.],.]
=> [2,1,3,4] => [2,1,3,4] => 2
[4,1,2,3] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => [1,4,3,2] => 6
[4,1,3,2] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => [1,3,4,2] => 3
[4,2,1,3] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => [1,2,4,3] => 2
[4,2,3,1] => [[[.,.],[.,.]],.]
=> [1,3,2,4] => [1,3,2,4] => 2
[4,3,1,2] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => [1,2,4,3] => 2
[4,3,2,1] => [[[[.,.],.],.],.]
=> [1,2,3,4] => [1,2,3,4] => 1
[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] => [[.,.],[[.,[.,.]],.]]
=> [1,4,3,5,2] => [1,4,3,5,2] => 8
[2,1,5,3,4] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => [1,3,5,4,2] => 8
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
=> [1,3,4,5,2] => [1,3,4,5,2] => 4
[3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]]
=> [1,5,4,3,2] => [1,5,4,3,2] => 24
[3,1,2,5,4] => [[.,.],[.,[[.,.],.]]]
=> [1,4,5,3,2] => [1,4,5,3,2] => 12
[3,1,4,2,5] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => [1,3,5,4,2] => 8
[3,1,4,5,2] => [[.,.],[[.,[.,.]],.]]
=> [1,4,3,5,2] => [1,4,3,5,2] => 8
[3,1,5,2,4] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => [1,3,5,4,2] => 8
[3,1,5,4,2] => [[.,.],[[[.,.],.],.]]
=> [1,3,4,5,2] => [1,3,4,5,2] => 4
[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
=> [1,2,5,4,3] => [1,2,5,4,3] => 6
[3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
=> [1,2,4,5,3] => [1,2,4,5,3] => 3
[3,2,4,1,5] => [[[.,.],[.,.]],[.,.]]
=> [1,3,2,5,4] => [1,3,2,5,4] => 4
[3,2,4,5,1] => [[[.,.],[.,[.,.]]],.]
=> [1,4,3,2,5] => [1,4,3,2,5] => 6
[3,2,5,1,4] => [[[.,.],[.,.]],[.,.]]
=> [1,3,2,5,4] => [1,3,2,5,4] => 4
Description
The number of signed permutations less than or equal to a signed permutation in left weak order.
Matching statistic: St000100
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000100: Posets ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000100: Posets ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Values
[1] => [.,.]
=> [1] => ([],1)
=> ? = 1
[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] => [[.,[.,.]],.]
=> [2,1,3] => ([(0,2),(1,2)],3)
=> 2
[3,1,2] => [[.,.],[.,.]]
=> [1,3,2] => ([(0,1),(0,2)],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] => [.,[[.,[.,.]],.]]
=> [3,2,4,1] => ([(1,3),(2,3)],4)
=> 8
[1,4,2,3] => [.,[[.,.],[.,.]]]
=> [2,4,3,1] => ([(1,2),(1,3)],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] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4
[2,3,4,1] => [[.,[.,[.,.]]],.]
=> [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> 6
[2,4,1,3] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4
[2,4,3,1] => [[.,[[.,.],.]],.]
=> [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> 3
[3,1,2,4] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> 6
[3,1,4,2] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> 3
[3,2,1,4] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> 2
[3,2,4,1] => [[[.,.],[.,.]],.]
=> [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[3,4,1,2] => [[.,[.,.]],[.,.]]
=> [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> 4
[3,4,2,1] => [[[.,[.,.]],.],.]
=> [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
=> 2
[4,1,2,3] => [[.,.],[.,[.,.]]]
=> [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> 6
[4,1,3,2] => [[.,.],[[.,.],.]]
=> [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
=> 3
[4,2,1,3] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> 2
[4,2,3,1] => [[[.,.],[.,.]],.]
=> [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
=> 2
[4,3,1,2] => [[[.,.],.],[.,.]]
=> [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
=> 2
[4,3,2,1] => [[[[.,.],.],.],.]
=> [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
=> 1
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
=> [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5)
=> 24
[2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
=> [1,4,5,3,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
=> 12
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> 8
[2,1,4,5,3] => [[.,.],[[.,[.,.]],.]]
=> [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> 8
[2,1,5,3,4] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> 8
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> 4
[3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]]
=> [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5)
=> 24
[3,1,2,5,4] => [[.,.],[.,[[.,.],.]]]
=> [1,4,5,3,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
=> 12
[3,1,4,2,5] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> 8
[3,1,4,5,2] => [[.,.],[[.,[.,.]],.]]
=> [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
=> 8
[3,1,5,2,4] => [[.,.],[[.,.],[.,.]]]
=> [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
=> 8
[3,1,5,4,2] => [[.,.],[[[.,.],.],.]]
=> [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
=> 4
[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
=> [1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
=> 6
[3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
=> [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
=> 3
[3,2,4,1,5] => [[[.,.],[.,.]],[.,.]]
=> [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[3,2,4,5,1] => [[[.,.],[.,[.,.]]],.]
=> [1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
=> 6
[3,2,5,1,4] => [[[.,.],[.,.]],[.,.]]
=> [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
=> 4
[3,2,5,4,1] => [[[.,.],[[.,.],.]],.]
=> [1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
=> 3
Description
The number of linear extensions of a poset.
Matching statistic: St001346
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
St001346: Permutations ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
St001346: Permutations ⟶ ℤResult quality: 99% ●values known / values provided: 99%●distinct values known / distinct values provided: 100%
Values
[1] => [.,.]
=> [.,.]
=> [1] => ? = 1
[1,2] => [.,[.,.]]
=> [[.,.],.]
=> [1,2] => 2
[2,1] => [[.,.],.]
=> [.,[.,.]]
=> [2,1] => 1
[1,2,3] => [.,[.,[.,.]]]
=> [[[.,.],.],.]
=> [1,2,3] => 6
[1,3,2] => [.,[[.,.],.]]
=> [[.,[.,.]],.]
=> [2,1,3] => 3
[2,1,3] => [[.,.],[.,.]]
=> [[.,.],[.,.]]
=> [3,1,2] => 2
[2,3,1] => [[.,[.,.]],.]
=> [.,[[.,.],.]]
=> [2,3,1] => 2
[3,1,2] => [[.,.],[.,.]]
=> [[.,.],[.,.]]
=> [3,1,2] => 2
[3,2,1] => [[[.,.],.],.]
=> [.,[.,[.,.]]]
=> [3,2,1] => 1
[1,2,3,4] => [.,[.,[.,[.,.]]]]
=> [[[[.,.],.],.],.]
=> [1,2,3,4] => 24
[1,2,4,3] => [.,[.,[[.,.],.]]]
=> [[[.,[.,.]],.],.]
=> [2,1,3,4] => 12
[1,3,2,4] => [.,[[.,.],[.,.]]]
=> [[[.,.],[.,.]],.]
=> [3,1,2,4] => 8
[1,3,4,2] => [.,[[.,[.,.]],.]]
=> [[.,[[.,.],.]],.]
=> [2,3,1,4] => 8
[1,4,2,3] => [.,[[.,.],[.,.]]]
=> [[[.,.],[.,.]],.]
=> [3,1,2,4] => 8
[1,4,3,2] => [.,[[[.,.],.],.]]
=> [[.,[.,[.,.]]],.]
=> [3,2,1,4] => 4
[2,1,3,4] => [[.,.],[.,[.,.]]]
=> [[[.,.],.],[.,.]]
=> [4,1,2,3] => 6
[2,1,4,3] => [[.,.],[[.,.],.]]
=> [[.,[.,.]],[.,.]]
=> [4,2,1,3] => 3
[2,3,1,4] => [[.,[.,.]],[.,.]]
=> [[.,.],[[.,.],.]]
=> [3,4,1,2] => 4
[2,3,4,1] => [[.,[.,[.,.]]],.]
=> [.,[[[.,.],.],.]]
=> [2,3,4,1] => 6
[2,4,1,3] => [[.,[.,.]],[.,.]]
=> [[.,.],[[.,.],.]]
=> [3,4,1,2] => 4
[2,4,3,1] => [[.,[[.,.],.]],.]
=> [.,[[.,[.,.]],.]]
=> [3,2,4,1] => 3
[3,1,2,4] => [[.,.],[.,[.,.]]]
=> [[[.,.],.],[.,.]]
=> [4,1,2,3] => 6
[3,1,4,2] => [[.,.],[[.,.],.]]
=> [[.,[.,.]],[.,.]]
=> [4,2,1,3] => 3
[3,2,1,4] => [[[.,.],.],[.,.]]
=> [[.,.],[.,[.,.]]]
=> [4,3,1,2] => 2
[3,2,4,1] => [[[.,.],[.,.]],.]
=> [.,[[.,.],[.,.]]]
=> [4,2,3,1] => 2
[3,4,1,2] => [[.,[.,.]],[.,.]]
=> [[.,.],[[.,.],.]]
=> [3,4,1,2] => 4
[3,4,2,1] => [[[.,[.,.]],.],.]
=> [.,[.,[[.,.],.]]]
=> [3,4,2,1] => 2
[4,1,2,3] => [[.,.],[.,[.,.]]]
=> [[[.,.],.],[.,.]]
=> [4,1,2,3] => 6
[4,1,3,2] => [[.,.],[[.,.],.]]
=> [[.,[.,.]],[.,.]]
=> [4,2,1,3] => 3
[4,2,1,3] => [[[.,.],.],[.,.]]
=> [[.,.],[.,[.,.]]]
=> [4,3,1,2] => 2
[4,2,3,1] => [[[.,.],[.,.]],.]
=> [.,[[.,.],[.,.]]]
=> [4,2,3,1] => 2
[4,3,1,2] => [[[.,.],.],[.,.]]
=> [[.,.],[.,[.,.]]]
=> [4,3,1,2] => 2
[4,3,2,1] => [[[[.,.],.],.],.]
=> [.,[.,[.,[.,.]]]]
=> [4,3,2,1] => 1
[2,1,3,4,5] => [[.,.],[.,[.,[.,.]]]]
=> [[[[.,.],.],.],[.,.]]
=> [5,1,2,3,4] => 24
[2,1,3,5,4] => [[.,.],[.,[[.,.],.]]]
=> [[[.,[.,.]],.],[.,.]]
=> [5,2,1,3,4] => 12
[2,1,4,3,5] => [[.,.],[[.,.],[.,.]]]
=> [[[.,.],[.,.]],[.,.]]
=> [5,3,1,2,4] => 8
[2,1,4,5,3] => [[.,.],[[.,[.,.]],.]]
=> [[.,[[.,.],.]],[.,.]]
=> [5,2,3,1,4] => 8
[2,1,5,3,4] => [[.,.],[[.,.],[.,.]]]
=> [[[.,.],[.,.]],[.,.]]
=> [5,3,1,2,4] => 8
[2,1,5,4,3] => [[.,.],[[[.,.],.],.]]
=> [[.,[.,[.,.]]],[.,.]]
=> [5,3,2,1,4] => 4
[3,1,2,4,5] => [[.,.],[.,[.,[.,.]]]]
=> [[[[.,.],.],.],[.,.]]
=> [5,1,2,3,4] => 24
[3,1,2,5,4] => [[.,.],[.,[[.,.],.]]]
=> [[[.,[.,.]],.],[.,.]]
=> [5,2,1,3,4] => 12
[3,1,4,2,5] => [[.,.],[[.,.],[.,.]]]
=> [[[.,.],[.,.]],[.,.]]
=> [5,3,1,2,4] => 8
[3,1,4,5,2] => [[.,.],[[.,[.,.]],.]]
=> [[.,[[.,.],.]],[.,.]]
=> [5,2,3,1,4] => 8
[3,1,5,2,4] => [[.,.],[[.,.],[.,.]]]
=> [[[.,.],[.,.]],[.,.]]
=> [5,3,1,2,4] => 8
[3,1,5,4,2] => [[.,.],[[[.,.],.],.]]
=> [[.,[.,[.,.]]],[.,.]]
=> [5,3,2,1,4] => 4
[3,2,1,4,5] => [[[.,.],.],[.,[.,.]]]
=> [[[.,.],.],[.,[.,.]]]
=> [5,4,1,2,3] => 6
[3,2,1,5,4] => [[[.,.],.],[[.,.],.]]
=> [[.,[.,.]],[.,[.,.]]]
=> [5,4,2,1,3] => 3
[3,2,4,1,5] => [[[.,.],[.,.]],[.,.]]
=> [[.,.],[[.,.],[.,.]]]
=> [5,3,4,1,2] => 4
[3,2,4,5,1] => [[[.,.],[.,[.,.]]],.]
=> [.,[[[.,.],.],[.,.]]]
=> [5,2,3,4,1] => 6
[3,2,5,1,4] => [[[.,.],[.,.]],[.,.]]
=> [[.,.],[[.,.],[.,.]]]
=> [5,3,4,1,2] => 4
[3,2,5,4,1] => [[[.,.],[[.,.],.]],.]
=> [.,[[.,[.,.]],[.,.]]]
=> [5,3,2,4,1] => 3
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.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!