Your data matches 3 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000415
Mapping
Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees
Mp00018: Binary trees —left border symmetry⟶ Binary trees
Mp00015: Binary trees —to ordered tree: right child = right brother⟶ Ordered trees
St000415: Ordered trees ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[],[]]
 => [.,[.,.]]
 => [.,[.,.]]
 => [[],[]]
 => 2
[[[]]]
 => [[.,.],.]
 => [[.,.],.]
 => [[[]]]
 => 1
[[],[],[]]
 => [.,[.,[.,.]]]
 => [.,[.,[.,.]]]
 => [[],[],[]]
 => 6
[[],[[]]]
 => [.,[[.,.],.]]
 => [.,[[.,.],.]]
 => [[],[[]]]
 => 2
[[[]],[]]
 => [[.,.],[.,.]]
 => [[.,[.,.]],.]
 => [[[],[]]]
 => 2
[[[],[]]]
 => [[.,[.,.]],.]
 => [[.,.],[.,.]]
 => [[[]],[]]
 => 2
[[[[]]]]
 => [[[.,.],.],.]
 => [[[.,.],.],.]
 => [[[[]]]]
 => 1
[[],[],[],[]]
 => [.,[.,[.,[.,.]]]]
 => [.,[.,[.,[.,.]]]]
 => [[],[],[],[]]
 => 24
[[],[],[[]]]
 => [.,[.,[[.,.],.]]]
 => [.,[.,[[.,.],.]]]
 => [[],[],[[]]]
 => 6
[[],[[]],[]]
 => [.,[[.,.],[.,.]]]
 => [.,[[.,[.,.]],.]]
 => [[],[[],[]]]
 => 4
[[],[[],[]]]
 => [.,[[.,[.,.]],.]]
 => [.,[[.,.],[.,.]]]
 => [[],[[]],[]]
 => 6
[[],[[[]]]]
 => [.,[[[.,.],.],.]]
 => [.,[[[.,.],.],.]]
 => [[],[[[]]]]
 => 2
[[[]],[],[]]
 => [[.,.],[.,[.,.]]]
 => [[.,[.,[.,.]]],.]
 => [[[],[],[]]]
 => 6
[[[]],[[]]]
 => [[.,.],[[.,.],.]]
 => [[.,[[.,.],.]],.]
 => [[[],[[]]]]
 => 2
[[[],[]],[]]
 => [[.,[.,.]],[.,.]]
 => [[.,[.,.]],[.,.]]
 => [[[],[]],[]]
 => 4
[[[[]]],[]]
 => [[[.,.],.],[.,.]]
 => [[[.,[.,.]],.],.]
 => [[[[],[]]]]
 => 2
[[[],[],[]]]
 => [[.,[.,[.,.]]],.]
 => [[.,.],[.,[.,.]]]
 => [[[]],[],[]]
 => 6
[[[],[[]]]]
 => [[.,[[.,.],.]],.]
 => [[.,.],[[.,.],.]]
 => [[[]],[[]]]
 => 2
[[[[]],[]]]
 => [[[.,.],[.,.]],.]
 => [[[.,.],[.,.]],.]
 => [[[[]],[]]]
 => 2
[[[[],[]]]]
 => [[[.,[.,.]],.],.]
 => [[[.,.],.],[.,.]]
 => [[[[]]],[]]
 => 2
[[[[[]]]]]
 => [[[[.,.],.],.],.]
 => [[[[.,.],.],.],.]
 => [[[[[]]]]]
 => 1
[[],[],[],[],[]]
 => [.,[.,[.,[.,[.,.]]]]]
 => [.,[.,[.,[.,[.,.]]]]]
 => [[],[],[],[],[]]
 => 120
[[],[],[],[[]]]
 => [.,[.,[.,[[.,.],.]]]]
 => [.,[.,[.,[[.,.],.]]]]
 => [[],[],[],[[]]]
 => 24
[[],[],[[]],[]]
 => [.,[.,[[.,.],[.,.]]]]
 => [.,[.,[[.,[.,.]],.]]]
 => [[],[],[[],[]]]
 => 12
[[],[],[[],[]]]
 => [.,[.,[[.,[.,.]],.]]]
 => [.,[.,[[.,.],[.,.]]]]
 => [[],[],[[]],[]]
 => 24
[[],[],[[[]]]]
 => [.,[.,[[[.,.],.],.]]]
 => [.,[.,[[[.,.],.],.]]]
 => [[],[],[[[]]]]
 => 6
[[],[[]],[],[]]
 => [.,[[.,.],[.,[.,.]]]]
 => [.,[[.,[.,[.,.]]],.]]
 => [[],[[],[],[]]]
 => 12
[[],[[]],[[]]]
 => [.,[[.,.],[[.,.],.]]]
 => [.,[[.,[[.,.],.]],.]]
 => [[],[[],[[]]]]
 => 4
[[],[[],[]],[]]
 => [.,[[.,[.,.]],[.,.]]]
 => [.,[[.,[.,.]],[.,.]]]
 => [[],[[],[]],[]]
 => 12
[[],[[[]]],[]]
 => [.,[[[.,.],.],[.,.]]]
 => [.,[[[.,[.,.]],.],.]]
 => [[],[[[],[]]]]
 => 4
[[],[[],[],[]]]
 => [.,[[.,[.,[.,.]]],.]]
 => [.,[[.,.],[.,[.,.]]]]
 => [[],[[]],[],[]]
 => 24
[[],[[],[[]]]]
 => [.,[[.,[[.,.],.]],.]]
 => [.,[[.,.],[[.,.],.]]]
 => [[],[[]],[[]]]
 => 6
[[],[[[]],[]]]
 => [.,[[[.,.],[.,.]],.]]
 => [.,[[[.,.],[.,.]],.]]
 => [[],[[[]],[]]]
 => 4
[[],[[[],[]]]]
 => [.,[[[.,[.,.]],.],.]]
 => [.,[[[.,.],.],[.,.]]]
 => [[],[[[]]],[]]
 => 6
[[],[[[[]]]]]
 => [.,[[[[.,.],.],.],.]]
 => [.,[[[[.,.],.],.],.]]
 => [[],[[[[]]]]]
 => 2
[[[]],[],[],[]]
 => [[.,.],[.,[.,[.,.]]]]
 => [[.,[.,[.,[.,.]]]],.]
 => [[[],[],[],[]]]
 => 24
[[[]],[],[[]]]
 => [[.,.],[.,[[.,.],.]]]
 => [[.,[.,[[.,.],.]]],.]
 => [[[],[],[[]]]]
 => 6
[[[]],[[]],[]]
 => [[.,.],[[.,.],[.,.]]]
 => [[.,[[.,[.,.]],.]],.]
 => [[[],[[],[]]]]
 => 4
[[[]],[[],[]]]
 => [[.,.],[[.,[.,.]],.]]
 => [[.,[[.,.],[.,.]]],.]
 => [[[],[[]],[]]]
 => 6
[[[]],[[[]]]]
 => [[.,.],[[[.,.],.],.]]
 => [[.,[[[.,.],.],.]],.]
 => [[[],[[[]]]]]
 => 2
[[[],[]],[],[]]
 => [[.,[.,.]],[.,[.,.]]]
 => [[.,[.,[.,.]]],[.,.]]
 => [[[],[],[]],[]]
 => 12
[[[[]]],[],[]]
 => [[[.,.],.],[.,[.,.]]]
 => [[[.,[.,[.,.]]],.],.]
 => [[[[],[],[]]]]
 => 6
[[[],[]],[[]]]
 => [[.,[.,.]],[[.,.],.]]
 => [[.,[[.,.],.]],[.,.]]
 => [[[],[[]]],[]]
 => 4
[[[[]]],[[]]]
 => [[[.,.],.],[[.,.],.]]
 => [[[.,[[.,.],.]],.],.]
 => [[[[],[[]]]]]
 => 2
[[[],[],[]],[]]
 => [[.,[.,[.,.]]],[.,.]]
 => [[.,[.,.]],[.,[.,.]]]
 => [[[],[]],[],[]]
 => 12
[[[],[[]]],[]]
 => [[.,[[.,.],.]],[.,.]]
 => [[.,[.,.]],[[.,.],.]]
 => [[[],[]],[[]]]
 => 4
[[[[]],[]],[]]
 => [[[.,.],[.,.]],[.,.]]
 => [[[.,[.,.]],[.,.]],.]
 => [[[[],[]],[]]]
 => 4
[[[[],[]]],[]]
 => [[[.,[.,.]],.],[.,.]]
 => [[[.,[.,.]],.],[.,.]]
 => [[[[],[]]],[]]
 => 4
[[[[[]]]],[]]
 => [[[[.,.],.],.],[.,.]]
 => [[[[.,[.,.]],.],.],.]
 => [[[[[],[]]]]]
 => 2
[[[],[],[],[]]]
 => [[.,[.,[.,[.,.]]]],.]
 => [[.,.],[.,[.,[.,.]]]]
 => [[[]],[],[],[]]
 => 24
Description
The size of the automorphism group of the rooted tree underlying the ordered tree.
Matching statistic: St001106
Mapping
Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001106: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[],[]]
 => [.,[.,.]]
 => [2,1] => ([],2)
 => 2
[[[]]]
 => [[.,.],.]
 => [1,2] => ([(0,1)],2)
 => 1
[[],[],[]]
 => [.,[.,[.,.]]]
 => [3,2,1] => ([],3)
 => 6
[[],[[]]]
 => [.,[[.,.],.]]
 => [2,3,1] => ([(1,2)],3)
 => 2
[[[]],[]]
 => [[.,.],[.,.]]
 => [1,3,2] => ([(0,1),(0,2)],3)
 => 2
[[[],[]]]
 => [[.,[.,.]],.]
 => [2,1,3] => ([(0,2),(1,2)],3)
 => 2
[[[[]]]]
 => [[[.,.],.],.]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => 1
[[],[],[],[]]
 => [.,[.,[.,[.,.]]]]
 => [4,3,2,1] => ([],4)
 => 24
[[],[],[[]]]
 => [.,[.,[[.,.],.]]]
 => [3,4,2,1] => ([(2,3)],4)
 => 6
[[],[[]],[]]
 => [.,[[.,.],[.,.]]]
 => [2,4,3,1] => ([(1,2),(1,3)],4)
 => 4
[[],[[],[]]]
 => [.,[[.,[.,.]],.]]
 => [3,2,4,1] => ([(1,3),(2,3)],4)
 => 6
[[],[[[]]]]
 => [.,[[[.,.],.],.]]
 => [2,3,4,1] => ([(1,2),(2,3)],4)
 => 2
[[[]],[],[]]
 => [[.,.],[.,[.,.]]]
 => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
 => 6
[[[]],[[]]]
 => [[.,.],[[.,.],.]]
 => [1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
 => 2
[[[],[]],[]]
 => [[.,[.,.]],[.,.]]
 => [2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 4
[[[[]]],[]]
 => [[[.,.],.],[.,.]]
 => [1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
 => 2
[[[],[],[]]]
 => [[.,[.,[.,.]]],.]
 => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
 => 6
[[[],[[]]]]
 => [[.,[[.,.],.]],.]
 => [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => 2
[[[[]],[]]]
 => [[[.,.],[.,.]],.]
 => [1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 2
[[[[],[]]]]
 => [[[.,[.,.]],.],.]
 => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => 2
[[[[[]]]]]
 => [[[[.,.],.],.],.]
 => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 1
[[],[],[],[],[]]
 => [.,[.,[.,[.,[.,.]]]]]
 => [5,4,3,2,1] => ([],5)
 => 120
[[],[],[],[[]]]
 => [.,[.,[.,[[.,.],.]]]]
 => [4,5,3,2,1] => ([(3,4)],5)
 => 24
[[],[],[[]],[]]
 => [.,[.,[[.,.],[.,.]]]]
 => [3,5,4,2,1] => ([(2,3),(2,4)],5)
 => 12
[[],[],[[],[]]]
 => [.,[.,[[.,[.,.]],.]]]
 => [4,3,5,2,1] => ([(2,4),(3,4)],5)
 => 24
[[],[],[[[]]]]
 => [.,[.,[[[.,.],.],.]]]
 => [3,4,5,2,1] => ([(2,3),(3,4)],5)
 => 6
[[],[[]],[],[]]
 => [.,[[.,.],[.,[.,.]]]]
 => [2,5,4,3,1] => ([(1,2),(1,3),(1,4)],5)
 => 12
[[],[[]],[[]]]
 => [.,[[.,.],[[.,.],.]]]
 => [2,4,5,3,1] => ([(1,3),(1,4),(4,2)],5)
 => 4
[[],[[],[]],[]]
 => [.,[[.,[.,.]],[.,.]]]
 => [3,2,5,4,1] => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 12
[[],[[[]]],[]]
 => [.,[[[.,.],.],[.,.]]]
 => [2,3,5,4,1] => ([(1,4),(4,2),(4,3)],5)
 => 4
[[],[[],[],[]]]
 => [.,[[.,[.,[.,.]]],.]]
 => [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
 => 24
[[],[[],[[]]]]
 => [.,[[.,[[.,.],.]],.]]
 => [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
 => 6
[[],[[[]],[]]]
 => [.,[[[.,.],[.,.]],.]]
 => [2,4,3,5,1] => ([(1,2),(1,3),(2,4),(3,4)],5)
 => 4
[[],[[[],[]]]]
 => [.,[[[.,[.,.]],.],.]]
 => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
 => 6
[[],[[[[]]]]]
 => [.,[[[[.,.],.],.],.]]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => 2
[[[]],[],[],[]]
 => [[.,.],[.,[.,[.,.]]]]
 => [1,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4)],5)
 => 24
[[[]],[],[[]]]
 => [[.,.],[.,[[.,.],.]]]
 => [1,4,5,3,2] => ([(0,2),(0,3),(0,4),(4,1)],5)
 => 6
[[[]],[[]],[]]
 => [[.,.],[[.,.],[.,.]]]
 => [1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
 => 4
[[[]],[[],[]]]
 => [[.,.],[[.,[.,.]],.]]
 => [1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 6
[[[]],[[[]]]]
 => [[.,.],[[[.,.],.],.]]
 => [1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 2
[[[],[]],[],[]]
 => [[.,[.,.]],[.,[.,.]]]
 => [2,1,5,4,3] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)
 => 12
[[[[]]],[],[]]
 => [[[.,.],.],[.,[.,.]]]
 => [1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
 => 6
[[[],[]],[[]]]
 => [[.,[.,.]],[[.,.],.]]
 => [2,1,4,5,3] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5)
 => 4
[[[[]]],[[]]]
 => [[[.,.],.],[[.,.],.]]
 => [1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
 => 2
[[[],[],[]],[]]
 => [[.,[.,[.,.]]],[.,.]]
 => [3,2,1,5,4] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 12
[[[],[[]]],[]]
 => [[.,[[.,.],.]],[.,.]]
 => [2,3,1,5,4] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5)
 => 4
[[[[]],[]],[]]
 => [[[.,.],[.,.]],[.,.]]
 => [1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 4
[[[[],[]]],[]]
 => [[[.,[.,.]],.],[.,.]]
 => [2,1,3,5,4] => ([(0,4),(1,4),(4,2),(4,3)],5)
 => 4
[[[[[]]]],[]]
 => [[[[.,.],.],.],[.,.]]
 => [1,2,3,5,4] => ([(0,3),(3,4),(4,1),(4,2)],5)
 => 2
[[[],[],[],[]]]
 => [[.,[.,[.,[.,.]]]],.]
 => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 24
Description
The number of supergreedy linear extensions of a poset. A linear extension of a poset P with elements $\{x_1,\dots,x_n\}$ is supergreedy, if it can be obtained by the following algorithm: * Step 1. Choose a minimal element $x_1$. * Step 2. Suppose $X=\{x_1,\dots,x_i\}$ have been chosen, let $M$ be the set of minimal elements of $P\setminus X$. If there is an element of $M$ which covers an element $x_j$ in $X$, then let $x_{i+1}$ be one of these such that $j$ is maximal; otherwise, choose $x_{i+1}$ to be any element of $M$. This statistic records the number of supergreedy linear extensions.
Matching statistic: St001346
Mapping
Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
St001346: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[],[]]
 => [.,[.,.]]
 => [2,1] => [1,2] => 2
[[[]]]
 => [[.,.],.]
 => [1,2] => [2,1] => 1
[[],[],[]]
 => [.,[.,[.,.]]]
 => [3,2,1] => [1,2,3] => 6
[[],[[]]]
 => [.,[[.,.],.]]
 => [2,3,1] => [1,3,2] => 2
[[[]],[]]
 => [[.,.],[.,.]]
 => [1,3,2] => [2,3,1] => 2
[[[],[]]]
 => [[.,[.,.]],.]
 => [2,1,3] => [3,1,2] => 2
[[[[]]]]
 => [[[.,.],.],.]
 => [1,2,3] => [3,2,1] => 1
[[],[],[],[]]
 => [.,[.,[.,[.,.]]]]
 => [4,3,2,1] => [1,2,3,4] => 24
[[],[],[[]]]
 => [.,[.,[[.,.],.]]]
 => [3,4,2,1] => [1,2,4,3] => 6
[[],[[]],[]]
 => [.,[[.,.],[.,.]]]
 => [2,4,3,1] => [1,3,4,2] => 4
[[],[[],[]]]
 => [.,[[.,[.,.]],.]]
 => [3,2,4,1] => [1,4,2,3] => 6
[[],[[[]]]]
 => [.,[[[.,.],.],.]]
 => [2,3,4,1] => [1,4,3,2] => 2
[[[]],[],[]]
 => [[.,.],[.,[.,.]]]
 => [1,4,3,2] => [2,3,4,1] => 6
[[[]],[[]]]
 => [[.,.],[[.,.],.]]
 => [1,3,4,2] => [2,4,3,1] => 2
[[[],[]],[]]
 => [[.,[.,.]],[.,.]]
 => [2,1,4,3] => [3,4,1,2] => 4
[[[[]]],[]]
 => [[[.,.],.],[.,.]]
 => [1,2,4,3] => [3,4,2,1] => 2
[[[],[],[]]]
 => [[.,[.,[.,.]]],.]
 => [3,2,1,4] => [4,1,2,3] => 6
[[[],[[]]]]
 => [[.,[[.,.],.]],.]
 => [2,3,1,4] => [4,1,3,2] => 2
[[[[]],[]]]
 => [[[.,.],[.,.]],.]
 => [1,3,2,4] => [4,2,3,1] => 2
[[[[],[]]]]
 => [[[.,[.,.]],.],.]
 => [2,1,3,4] => [4,3,1,2] => 2
[[[[[]]]]]
 => [[[[.,.],.],.],.]
 => [1,2,3,4] => [4,3,2,1] => 1
[[],[],[],[],[]]
 => [.,[.,[.,[.,[.,.]]]]]
 => [5,4,3,2,1] => [1,2,3,4,5] => 120
[[],[],[],[[]]]
 => [.,[.,[.,[[.,.],.]]]]
 => [4,5,3,2,1] => [1,2,3,5,4] => 24
[[],[],[[]],[]]
 => [.,[.,[[.,.],[.,.]]]]
 => [3,5,4,2,1] => [1,2,4,5,3] => 12
[[],[],[[],[]]]
 => [.,[.,[[.,[.,.]],.]]]
 => [4,3,5,2,1] => [1,2,5,3,4] => 24
[[],[],[[[]]]]
 => [.,[.,[[[.,.],.],.]]]
 => [3,4,5,2,1] => [1,2,5,4,3] => 6
[[],[[]],[],[]]
 => [.,[[.,.],[.,[.,.]]]]
 => [2,5,4,3,1] => [1,3,4,5,2] => 12
[[],[[]],[[]]]
 => [.,[[.,.],[[.,.],.]]]
 => [2,4,5,3,1] => [1,3,5,4,2] => 4
[[],[[],[]],[]]
 => [.,[[.,[.,.]],[.,.]]]
 => [3,2,5,4,1] => [1,4,5,2,3] => 12
[[],[[[]]],[]]
 => [.,[[[.,.],.],[.,.]]]
 => [2,3,5,4,1] => [1,4,5,3,2] => 4
[[],[[],[],[]]]
 => [.,[[.,[.,[.,.]]],.]]
 => [4,3,2,5,1] => [1,5,2,3,4] => 24
[[],[[],[[]]]]
 => [.,[[.,[[.,.],.]],.]]
 => [3,4,2,5,1] => [1,5,2,4,3] => 6
[[],[[[]],[]]]
 => [.,[[[.,.],[.,.]],.]]
 => [2,4,3,5,1] => [1,5,3,4,2] => 4
[[],[[[],[]]]]
 => [.,[[[.,[.,.]],.],.]]
 => [3,2,4,5,1] => [1,5,4,2,3] => 6
[[],[[[[]]]]]
 => [.,[[[[.,.],.],.],.]]
 => [2,3,4,5,1] => [1,5,4,3,2] => 2
[[[]],[],[],[]]
 => [[.,.],[.,[.,[.,.]]]]
 => [1,5,4,3,2] => [2,3,4,5,1] => 24
[[[]],[],[[]]]
 => [[.,.],[.,[[.,.],.]]]
 => [1,4,5,3,2] => [2,3,5,4,1] => 6
[[[]],[[]],[]]
 => [[.,.],[[.,.],[.,.]]]
 => [1,3,5,4,2] => [2,4,5,3,1] => 4
[[[]],[[],[]]]
 => [[.,.],[[.,[.,.]],.]]
 => [1,4,3,5,2] => [2,5,3,4,1] => 6
[[[]],[[[]]]]
 => [[.,.],[[[.,.],.],.]]
 => [1,3,4,5,2] => [2,5,4,3,1] => 2
[[[],[]],[],[]]
 => [[.,[.,.]],[.,[.,.]]]
 => [2,1,5,4,3] => [3,4,5,1,2] => 12
[[[[]]],[],[]]
 => [[[.,.],.],[.,[.,.]]]
 => [1,2,5,4,3] => [3,4,5,2,1] => 6
[[[],[]],[[]]]
 => [[.,[.,.]],[[.,.],.]]
 => [2,1,4,5,3] => [3,5,4,1,2] => 4
[[[[]]],[[]]]
 => [[[.,.],.],[[.,.],.]]
 => [1,2,4,5,3] => [3,5,4,2,1] => 2
[[[],[],[]],[]]
 => [[.,[.,[.,.]]],[.,.]]
 => [3,2,1,5,4] => [4,5,1,2,3] => 12
[[[],[[]]],[]]
 => [[.,[[.,.],.]],[.,.]]
 => [2,3,1,5,4] => [4,5,1,3,2] => 4
[[[[]],[]],[]]
 => [[[.,.],[.,.]],[.,.]]
 => [1,3,2,5,4] => [4,5,2,3,1] => 4
[[[[],[]]],[]]
 => [[[.,[.,.]],.],[.,.]]
 => [2,1,3,5,4] => [4,5,3,1,2] => 4
[[[[[]]]],[]]
 => [[[[.,.],.],.],[.,.]]
 => [1,2,3,5,4] => [4,5,3,2,1] => 2
[[[],[],[],[]]]
 => [[.,[.,[.,[.,.]]]],.]
 => [4,3,2,1,5] => [5,1,2,3,4] => 24
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.