Your data matches 4 different statistics following compositions of up to 3 maps.
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Matching statistic: St000410
(load all 2 compositions to match this statistic)
Mapping
St000410: Ordered trees ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[]]
 => 2
[[],[]]
 => 3
[[[]]]
 => 6
[[],[],[]]
 => 4
[[],[[]]]
 => 8
[[[]],[]]
 => 8
[[[],[]]]
 => 12
[[[[]]]]
 => 24
[[],[],[],[]]
 => 5
[[],[],[[]]]
 => 10
[[],[[]],[]]
 => 10
[[],[[],[]]]
 => 15
[[],[[[]]]]
 => 30
[[[]],[],[]]
 => 10
[[[]],[[]]]
 => 20
[[[],[]],[]]
 => 15
[[[[]]],[]]
 => 30
[[[],[],[]]]
 => 20
[[[],[[]]]]
 => 40
[[[[]],[]]]
 => 40
[[[[],[]]]]
 => 60
[[[[[]]]]]
 => 120
[[],[],[],[],[]]
 => 6
[[],[],[],[[]]]
 => 12
[[],[],[[]],[]]
 => 12
[[],[],[[],[]]]
 => 18
[[],[],[[[]]]]
 => 36
[[],[[]],[],[]]
 => 12
[[],[[]],[[]]]
 => 24
[[],[[],[]],[]]
 => 18
[[],[[[]]],[]]
 => 36
[[],[[],[],[]]]
 => 24
[[],[[],[[]]]]
 => 48
[[],[[[]],[]]]
 => 48
[[],[[[],[]]]]
 => 72
[[],[[[[]]]]]
 => 144
[[[]],[],[],[]]
 => 12
[[[]],[],[[]]]
 => 24
[[[]],[[]],[]]
 => 24
[[[]],[[],[]]]
 => 36
[[[]],[[[]]]]
 => 72
[[[],[]],[],[]]
 => 18
[[[[]]],[],[]]
 => 36
[[[],[]],[[]]]
 => 36
[[[[]]],[[]]]
 => 72
[[[],[],[]],[]]
 => 24
[[[],[[]]],[]]
 => 48
[[[[]],[]],[]]
 => 48
[[[[],[]]],[]]
 => 72
[[[[[]]]],[]]
 => 144
Description
The tree factorial of an ordered tree.
Matching statistic: St001813
Mapping
Mp00047: Ordered trees —to poset⟶ Posets
Mp00125: Posets —dual poset⟶ Posets
St001813: Posets ⟶ ℤResult quality: 9% ●values known / values provided: 9%●distinct values known / distinct values provided: 26%
Values
[[]]
 => ([(0,1)],2)
 => ([(0,1)],2)
 => 2
[[],[]]
 => ([(0,2),(1,2)],3)
 => ([(0,1),(0,2)],3)
 => 3
[[[]]]
 => ([(0,2),(2,1)],3)
 => ([(0,2),(2,1)],3)
 => 6
[[],[],[]]
 => ([(0,3),(1,3),(2,3)],4)
 => ([(0,1),(0,2),(0,3)],4)
 => 4
[[],[[]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(3,1)],4)
 => 8
[[[]],[]]
 => ([(0,3),(1,2),(2,3)],4)
 => ([(0,2),(0,3),(3,1)],4)
 => 8
[[[],[]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ([(0,3),(3,1),(3,2)],4)
 => 12
[[[[]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => ([(0,3),(2,1),(3,2)],4)
 => 24
[[],[],[],[]]
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(0,1),(0,2),(0,3),(0,4)],5)
 => 5
[[],[],[[]]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(4,1)],5)
 => 10
[[],[[]],[]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(4,1)],5)
 => 10
[[],[[],[]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => 15
[[],[[[]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 30
[[[]],[],[]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(0,2),(0,3),(0,4),(4,1)],5)
 => 10
[[[]],[[]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ([(0,3),(0,4),(3,2),(4,1)],5)
 => 20
[[[],[]],[]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ([(0,3),(0,4),(4,1),(4,2)],5)
 => 15
[[[[]]],[]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 30
[[[],[],[]]]
 => ([(0,4),(1,4),(2,4),(4,3)],5)
 => ([(0,4),(4,1),(4,2),(4,3)],5)
 => 20
[[[],[[]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,4),(3,2),(4,1),(4,3)],5)
 => 40
[[[[]],[]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ([(0,4),(3,2),(4,1),(4,3)],5)
 => 40
[[[[],[]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ([(0,3),(3,4),(4,1),(4,2)],5)
 => 60
[[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 120
[[],[],[],[],[]]
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
 => 6
[[],[],[],[[]]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => 12
[[],[],[[]],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => 12
[[],[],[[],[]]]
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => 18
[[],[],[[[]]]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
 => 36
[[],[[]],[],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => 12
[[],[[]],[[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => 24
[[],[[],[]],[]]
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => 18
[[],[[[]]],[]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
 => 36
[[],[[],[],[]]]
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => 24
[[],[[],[[]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
 => 48
[[],[[[]],[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
 => 48
[[],[[[],[]]]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
 => 72
[[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => 144
[[[]],[],[],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
 => 12
[[[]],[],[[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => 24
[[[]],[[]],[]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6)
 => 24
[[[]],[[],[]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
 => 36
[[[]],[[[]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => 72
[[[],[]],[],[]]
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ([(0,3),(0,4),(0,5),(5,1),(5,2)],6)
 => 18
[[[[]]],[],[]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6)
 => 36
[[[],[]],[[]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => ([(0,4),(0,5),(4,3),(5,1),(5,2)],6)
 => 36
[[[[]]],[[]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => ([(0,4),(0,5),(3,2),(4,3),(5,1)],6)
 => 72
[[[],[],[]],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ([(0,4),(0,5),(5,1),(5,2),(5,3)],6)
 => 24
[[[],[[]]],[]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
 => 48
[[[[]],[]],[]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ([(0,3),(0,5),(4,2),(5,1),(5,4)],6)
 => 48
[[[[],[]]],[]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ([(0,3),(0,4),(4,5),(5,1),(5,2)],6)
 => 72
[[[[[]]]],[]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ([(0,2),(0,5),(3,4),(4,1),(5,3)],6)
 => 144
[[],[],[[],[[]]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
 => ? = 56
[[],[],[[[]],[]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
 => ? = 56
[[],[],[[[[]]]]]
 => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)
 => ? = 168
[[],[[]],[[[]]]]
 => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
 => ? = 84
[[],[[[]]],[[]]]
 => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
 => ? = 84
[[],[[],[[]]],[]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
 => ? = 56
[[],[[[]],[]],[]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
 => ? = 56
[[],[[[[]]]],[]]
 => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)
 => ? = 168
[[],[[],[],[[]]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
 => ? = 70
[[],[[],[[]],[]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
 => ? = 70
[[],[[],[[],[]]]]
 => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
 => ? = 105
[[],[[],[[[]]]]]
 => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
 => ? = 210
[[],[[[]],[],[]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
 => ? = 70
[[],[[[]],[[]]]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
 => ([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7)
 => ? = 140
[[],[[[],[]],[]]]
 => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
 => ? = 105
[[],[[[[]]],[]]]
 => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
 => ? = 210
[[],[[[],[],[]]]]
 => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
 => ([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7)
 => ? = 140
[[],[[[],[[]]]]]
 => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
 => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
 => ? = 280
[[],[[[[]],[]]]]
 => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
 => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
 => ? = 280
[[],[[[[],[]]]]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)
 => ([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)
 => ? = 420
[[],[[[[[]]]]]]
 => ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
 => ([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)
 => ? = 840
[[[]],[],[[[]]]]
 => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
 => ? = 84
[[[]],[[[]]],[]]
 => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
 => ? = 84
[[[]],[[],[[]]]]
 => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)
 => ? = 112
[[[]],[[[]],[]]]
 => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)
 => ? = 112
[[[]],[[[],[]]]]
 => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
 => ([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7)
 => ? = 168
[[[]],[[[[]]]]]
 => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ? = 336
[[[[]]],[],[[]]]
 => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
 => ? = 84
[[[[]]],[[]],[]]
 => ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
 => ([(0,3),(0,5),(0,6),(4,1),(5,2),(6,4)],7)
 => ? = 84
[[[],[]],[[[]]]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7)
 => ? = 126
[[[[]]],[[],[]]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,6),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,4),(6,1),(6,2)],7)
 => ? = 126
[[[[]]],[[[]]]]
 => ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
 => ([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)
 => ? = 252
[[[],[[]]],[],[]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
 => ? = 56
[[[[]],[]],[],[]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)
 => ? = 56
[[[[[]]]],[],[]]
 => ([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)
 => ([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)
 => ? = 168
[[[],[[]]],[[]]]
 => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)
 => ? = 112
[[[[]],[]],[[]]]
 => ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
 => ([(0,5),(0,6),(4,3),(5,1),(6,2),(6,4)],7)
 => ? = 112
[[[[],[]]],[[]]]
 => ([(0,5),(1,5),(2,3),(3,6),(4,6),(5,4)],7)
 => ([(0,4),(0,5),(4,3),(5,6),(6,1),(6,2)],7)
 => ? = 168
[[[[[]]]],[[]]]
 => ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
 => ([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)
 => ? = 336
[[[],[],[[]]],[]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
 => ? = 70
[[[],[[]],[]],[]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
 => ? = 70
[[[],[[],[]]],[]]
 => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
 => ? = 105
[[[],[[[]]]],[]]
 => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
 => ? = 210
[[[[]],[],[]],[]]
 => ([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)
 => ? = 70
[[[[]],[[]]],[]]
 => ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
 => ([(0,3),(0,6),(4,2),(5,1),(6,4),(6,5)],7)
 => ? = 140
[[[[],[]],[]],[]]
 => ([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)
 => ([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)
 => ? = 105
[[[[[]]],[]],[]]
 => ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
 => ([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)
 => ? = 210
[[[[],[],[]]],[]]
 => ([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)
 => ([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7)
 => ? = 140
[[[[],[[]]]],[]]
 => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
 => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
 => ? = 280
[[[[[]],[]]],[]]
 => ([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)
 => ([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)
 => ? = 280
Description
The product of the sizes of the principal order filters in a poset.
Matching statistic: St000110
(load all 2 compositions to match this statistic)
Mapping
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
St000110: Permutations ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 37%
Values
[[]]
 => [1,0]
 => [1,1,0,0]
 => [2,1] => 2
[[],[]]
 => [1,0,1,0]
 => [1,1,0,1,0,0]
 => [2,3,1] => 3
[[[]]]
 => [1,1,0,0]
 => [1,1,1,0,0,0]
 => [3,2,1] => 6
[[],[],[]]
 => [1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [2,3,4,1] => 4
[[],[[]]]
 => [1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [2,4,3,1] => 8
[[[]],[]]
 => [1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [3,2,4,1] => 8
[[[],[]]]
 => [1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [3,4,2,1] => 12
[[[[]]]]
 => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [4,3,2,1] => 24
[[],[],[],[]]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,1] => 5
[[],[],[[]]]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [2,3,5,4,1] => 10
[[],[[]],[]]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [2,4,3,5,1] => 10
[[],[[],[]]]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [2,4,5,3,1] => 15
[[],[[[]]]]
 => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [2,5,4,3,1] => 30
[[[]],[],[]]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [3,2,4,5,1] => 10
[[[]],[[]]]
 => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [3,2,5,4,1] => 20
[[[],[]],[]]
 => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [3,4,2,5,1] => 15
[[[[]]],[]]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,3,2,5,1] => 30
[[[],[],[]]]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [3,4,5,2,1] => 20
[[[],[[]]]]
 => [1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [3,5,4,2,1] => 40
[[[[]],[]]]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [4,3,5,2,1] => 40
[[[[],[]]]]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [4,5,3,2,1] => 60
[[[[[]]]]]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [5,4,3,2,1] => 120
[[],[],[],[],[]]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [2,3,4,5,6,1] => 6
[[],[],[],[[]]]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [2,3,4,6,5,1] => 12
[[],[],[[]],[]]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [2,3,5,4,6,1] => 12
[[],[],[[],[]]]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [2,3,5,6,4,1] => 18
[[],[],[[[]]]]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [2,3,6,5,4,1] => 36
[[],[[]],[],[]]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [2,4,3,5,6,1] => 12
[[],[[]],[[]]]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [2,4,3,6,5,1] => 24
[[],[[],[]],[]]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [2,4,5,3,6,1] => 18
[[],[[[]]],[]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [2,5,4,3,6,1] => 36
[[],[[],[],[]]]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [2,4,5,6,3,1] => 24
[[],[[],[[]]]]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [2,4,6,5,3,1] => 48
[[],[[[]],[]]]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [2,5,4,6,3,1] => 48
[[],[[[],[]]]]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [2,5,6,4,3,1] => 72
[[],[[[[]]]]]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,6,5,4,3,1] => 144
[[[]],[],[],[]]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [3,2,4,5,6,1] => 12
[[[]],[],[[]]]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [3,2,4,6,5,1] => 24
[[[]],[[]],[]]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [3,2,5,4,6,1] => 24
[[[]],[[],[]]]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => [3,2,5,6,4,1] => 36
[[[]],[[[]]]]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [3,2,6,5,4,1] => 72
[[[],[]],[],[]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [3,4,2,5,6,1] => 18
[[[[]]],[],[]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [4,3,2,5,6,1] => 36
[[[],[]],[[]]]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => [3,4,2,6,5,1] => 36
[[[[]]],[[]]]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [4,3,2,6,5,1] => 72
[[[],[],[]],[]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [3,4,5,2,6,1] => 24
[[[],[[]]],[]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [3,5,4,2,6,1] => 48
[[[[]],[]],[]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => [4,3,5,2,6,1] => 48
[[[[],[]]],[]]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [4,5,3,2,6,1] => 72
[[[[[]]]],[]]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [5,4,3,2,6,1] => 144
[[],[],[],[],[[]]]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => [2,3,4,5,7,6,1] => ? = 14
[[],[],[],[[]],[]]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
 => [2,3,4,6,5,7,1] => ? = 14
[[],[],[],[[],[]]]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [2,3,4,6,7,5,1] => ? = 21
[[],[],[],[[[]]]]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
 => [2,3,4,7,6,5,1] => ? = 42
[[],[],[[]],[],[]]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
 => [2,3,5,4,6,7,1] => ? = 14
[[],[],[[]],[[]]]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
 => [2,3,5,4,7,6,1] => ? = 28
[[],[],[[],[]],[]]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
 => [2,3,5,6,4,7,1] => ? = 21
[[],[],[[[]]],[]]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,1,0,0]
 => [2,3,6,5,4,7,1] => ? = 42
[[],[],[[],[],[]]]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [2,3,5,6,7,4,1] => ? = 28
[[],[],[[],[[]]]]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,1,1,0,0,0,0]
 => [2,3,5,7,6,4,1] => ? = 56
[[],[],[[[]],[]]]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,1,1,1,0,0,1,0,0,0]
 => [2,3,6,5,7,4,1] => ? = 56
[[],[],[[[],[]]]]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
 => [2,3,6,7,5,4,1] => ? = 84
[[],[],[[[[]]]]]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => [2,3,7,6,5,4,1] => ? = 168
[[],[[]],[],[],[]]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
 => [2,4,3,5,6,7,1] => ? = 14
[[],[[]],[],[[]]]
 => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,0,1,1,0,0,0]
 => [2,4,3,5,7,6,1] => ? = 28
[[],[[]],[[]],[]]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
 => [2,4,3,6,5,7,1] => ? = 28
[[],[[]],[[],[]]]
 => [1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,1,0,0,0]
 => [2,4,3,6,7,5,1] => ? = 42
[[],[[]],[[[]]]]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
 => [2,4,3,7,6,5,1] => ? = 84
[[],[[],[]],[],[]]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,1,0,0]
 => [2,4,5,3,6,7,1] => ? = 21
[[],[[[]]],[],[]]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,1,0,0]
 => [2,5,4,3,6,7,1] => ? = 42
[[],[[],[]],[[]]]
 => [1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,1,0,0,1,1,0,0,0]
 => [2,4,5,3,7,6,1] => ? = 42
[[],[[[]]],[[]]]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
 => [2,5,4,3,7,6,1] => ? = 84
[[],[[],[],[]],[]]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
 => [2,4,5,6,3,7,1] => ? = 28
[[],[[],[[]]],[]]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
 => [2,4,6,5,3,7,1] => ? = 56
[[],[[[]],[]],[]]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,1,0,0,1,0,0]
 => [2,5,4,6,3,7,1] => ? = 56
[[],[[[],[]]],[]]
 => [1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,1,0,0,0,1,0,0]
 => [2,5,6,4,3,7,1] => ? = 84
[[],[[[[]]]],[]]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
 => [2,6,5,4,3,7,1] => ? = 168
[[],[[],[],[],[]]]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => [2,4,5,6,7,3,1] => ? = 35
[[],[[],[],[[]]]]
 => [1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,0,1,1,0,0,0,0]
 => [2,4,5,7,6,3,1] => ? = 70
[[],[[],[[]],[]]]
 => [1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
 => [2,4,6,5,7,3,1] => ? = 70
[[],[[],[[],[]]]]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,1,0,0,0,0]
 => [2,4,6,7,5,3,1] => ? = 105
[[],[[],[[[]]]]]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
 => [2,4,7,6,5,3,1] => ? = 210
[[],[[[]],[],[]]]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,1,0,0,0]
 => [2,5,4,6,7,3,1] => ? = 70
[[],[[[]],[[]]]]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
 => [2,5,4,7,6,3,1] => ? = 140
[[],[[[],[]],[]]]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,1,0,0,1,0,0,0]
 => [2,5,6,4,7,3,1] => ? = 105
[[],[[[[]]],[]]]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,1,1,1,0,0,0,1,0,0,0]
 => [2,6,5,4,7,3,1] => ? = 210
[[],[[[],[],[]]]]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
 => [2,5,6,7,4,3,1] => ? = 140
[[],[[[],[[]]]]]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,1,0,1,1,0,0,0,0,0]
 => [2,5,7,6,4,3,1] => ? = 280
[[],[[[[]],[]]]]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
 => [2,6,5,7,4,3,1] => ? = 280
[[],[[[[],[]]]]]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
 => [2,6,7,5,4,3,1] => ? = 420
[[],[[[[[]]]]]]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => [2,7,6,5,4,3,1] => ? = 840
[[[]],[],[],[[]]]
 => [1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
 => [3,2,4,5,7,6,1] => ? = 28
[[[]],[],[[]],[]]
 => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,1,1,0,0,1,0,0]
 => [3,2,4,6,5,7,1] => ? = 28
[[[]],[],[[],[]]]
 => [1,1,0,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,1,0,0,0]
 => [3,2,4,6,7,5,1] => ? = 42
[[[]],[],[[[]]]]
 => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
 => [3,2,4,7,6,5,1] => ? = 84
[[[]],[[]],[],[]]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,1,0,0]
 => [3,2,5,4,6,7,1] => ? = 28
[[[]],[[]],[[]]]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,1,1,0,0,0]
 => [3,2,5,4,7,6,1] => ? = 56
[[[]],[[],[]],[]]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,1,0,0,1,0,0]
 => [3,2,5,6,4,7,1] => ? = 42
[[[]],[[[]]],[]]
 => [1,1,0,0,1,1,1,0,0,0,1,0]
 => [1,1,1,0,0,1,1,1,0,0,0,1,0,0]
 => [3,2,6,5,4,7,1] => ? = 84
[[[]],[[],[],[]]]
 => [1,1,0,0,1,1,0,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,1,0,0,0]
 => [3,2,5,6,7,4,1] => ? = 56
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
Mapping
Mp00051: Ordered trees —to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00025: Dyck paths —to 132-avoiding permutation⟶ Permutations
St001346: Permutations ⟶ ℤResult quality: 5% ●values known / values provided: 5%●distinct values known / distinct values provided: 18%
Values
[[]]
 => [1,0]
 => [1,1,0,0]
 => [1,2] => 2
[[],[]]
 => [1,0,1,0]
 => [1,1,0,1,0,0]
 => [2,1,3] => 3
[[[]]]
 => [1,1,0,0]
 => [1,1,1,0,0,0]
 => [1,2,3] => 6
[[],[],[]]
 => [1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [3,2,1,4] => 4
[[],[[]]]
 => [1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [2,3,1,4] => 8
[[[]],[]]
 => [1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [3,1,2,4] => 8
[[[],[]]]
 => [1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [2,1,3,4] => 12
[[[[]]]]
 => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,2,3,4] => 24
[[],[],[],[]]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [4,3,2,1,5] => 5
[[],[],[[]]]
 => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [3,4,2,1,5] => 10
[[],[[]],[]]
 => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [4,2,3,1,5] => 10
[[],[[],[]]]
 => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [3,2,4,1,5] => 15
[[],[[[]]]]
 => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [2,3,4,1,5] => 30
[[[]],[],[]]
 => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [4,3,1,2,5] => 10
[[[]],[[]]]
 => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [3,4,1,2,5] => 20
[[[],[]],[]]
 => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [4,2,1,3,5] => 15
[[[[]]],[]]
 => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [4,1,2,3,5] => 30
[[[],[],[]]]
 => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [3,2,1,4,5] => 20
[[[],[[]]]]
 => [1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [2,3,1,4,5] => 40
[[[[]],[]]]
 => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [3,1,2,4,5] => 40
[[[[],[]]]]
 => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [2,1,3,4,5] => 60
[[[[[]]]]]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,2,3,4,5] => 120
[[],[],[],[],[]]
 => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [5,4,3,2,1,6] => 6
[[],[],[],[[]]]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [4,5,3,2,1,6] => 12
[[],[],[[]],[]]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [5,3,4,2,1,6] => 12
[[],[],[[],[]]]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [4,3,5,2,1,6] => 18
[[],[],[[[]]]]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [3,4,5,2,1,6] => 36
[[],[[]],[],[]]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [5,4,2,3,1,6] => 12
[[],[[]],[[]]]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [4,5,2,3,1,6] => 24
[[],[[],[]],[]]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [5,3,2,4,1,6] => 18
[[],[[[]]],[]]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [5,2,3,4,1,6] => 36
[[],[[],[],[]]]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [4,3,2,5,1,6] => 24
[[],[[],[[]]]]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [3,4,2,5,1,6] => 48
[[],[[[]],[]]]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [4,2,3,5,1,6] => 48
[[],[[[],[]]]]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [3,2,4,5,1,6] => 72
[[],[[[[]]]]]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [2,3,4,5,1,6] => 144
[[[]],[],[],[]]
 => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [5,4,3,1,2,6] => 12
[[[]],[],[[]]]
 => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [4,5,3,1,2,6] => 24
[[[]],[[]],[]]
 => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [5,3,4,1,2,6] => 24
[[[]],[[],[]]]
 => [1,1,0,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,1,0,1,0,0,0]
 => [4,3,5,1,2,6] => 36
[[[]],[[[]]]]
 => [1,1,0,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,1,1,0,0,0,0]
 => [3,4,5,1,2,6] => 72
[[[],[]],[],[]]
 => [1,1,0,1,0,0,1,0,1,0]
 => [1,1,1,0,1,0,0,1,0,1,0,0]
 => [5,4,2,1,3,6] => 18
[[[[]]],[],[]]
 => [1,1,1,0,0,0,1,0,1,0]
 => [1,1,1,1,0,0,0,1,0,1,0,0]
 => [5,4,1,2,3,6] => 36
[[[],[]],[[]]]
 => [1,1,0,1,0,0,1,1,0,0]
 => [1,1,1,0,1,0,0,1,1,0,0,0]
 => [4,5,2,1,3,6] => 36
[[[[]]],[[]]]
 => [1,1,1,0,0,0,1,1,0,0]
 => [1,1,1,1,0,0,0,1,1,0,0,0]
 => [4,5,1,2,3,6] => 72
[[[],[],[]],[]]
 => [1,1,0,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,1,0,0,1,0,0]
 => [5,3,2,1,4,6] => 24
[[[],[[]]],[]]
 => [1,1,0,1,1,0,0,0,1,0]
 => [1,1,1,0,1,1,0,0,0,1,0,0]
 => [5,2,3,1,4,6] => 48
[[[[]],[]],[]]
 => [1,1,1,0,0,1,0,0,1,0]
 => [1,1,1,1,0,0,1,0,0,1,0,0]
 => [5,3,1,2,4,6] => 48
[[[[],[]]],[]]
 => [1,1,1,0,1,0,0,0,1,0]
 => [1,1,1,1,0,1,0,0,0,1,0,0]
 => [5,2,1,3,4,6] => 72
[[[[[]]]],[]]
 => [1,1,1,1,0,0,0,0,1,0]
 => [1,1,1,1,1,0,0,0,0,1,0,0]
 => [5,1,2,3,4,6] => 144
[[],[],[],[],[],[]]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,1,0,0]
 => [6,5,4,3,2,1,7] => ? = 7
[[],[],[],[],[[]]]
 => [1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,0,1,1,0,0,0]
 => [5,6,4,3,2,1,7] => ? = 14
[[],[],[],[[]],[]]
 => [1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,0,1,1,0,0,1,0,0]
 => [6,4,5,3,2,1,7] => ? = 14
[[],[],[],[[],[]]]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,1,0,0,0]
 => [5,4,6,3,2,1,7] => ? = 21
[[],[],[],[[[]]]]
 => [1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,0,1,1,1,0,0,0,0]
 => [4,5,6,3,2,1,7] => ? = 42
[[],[],[[]],[],[]]
 => [1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,1,0,0]
 => [6,5,3,4,2,1,7] => ? = 14
[[],[],[[]],[[]]]
 => [1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,1,1,0,0,0]
 => [5,6,3,4,2,1,7] => ? = 28
[[],[],[[],[]],[]]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,1,0,0,1,0,0]
 => [6,4,3,5,2,1,7] => ? = 21
[[],[],[[[]]],[]]
 => [1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,0,1,1,1,0,0,0,1,0,0]
 => [6,3,4,5,2,1,7] => ? = 42
[[],[],[[],[],[]]]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,1,0,0,0]
 => [5,4,3,6,2,1,7] => ? = 28
[[],[],[[],[[]]]]
 => [1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,0,1,1,0,1,1,0,0,0,0]
 => [4,5,3,6,2,1,7] => ? = 56
[[],[],[[[]],[]]]
 => [1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,1,1,1,0,0,1,0,0,0]
 => [5,3,4,6,2,1,7] => ? = 56
[[],[],[[[],[]]]]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,1,0,0,0,0]
 => [4,3,5,6,2,1,7] => ? = 84
[[],[],[[[[]]]]]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,0,1,1,1,1,0,0,0,0,0]
 => [3,4,5,6,2,1,7] => ? = 168
[[],[[]],[],[],[]]
 => [1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,1,0,0]
 => [6,5,4,2,3,1,7] => ? = 14
[[],[[]],[],[[]]]
 => [1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,0,1,1,0,0,0]
 => [5,6,4,2,3,1,7] => ? = 28
[[],[[]],[[]],[]]
 => [1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,1,0,0,1,0,0]
 => [6,4,5,2,3,1,7] => ? = 28
[[],[[]],[[],[]]]
 => [1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,1,0,0,0]
 => [5,4,6,2,3,1,7] => ? = 42
[[],[[]],[[[]]]]
 => [1,0,1,1,0,0,1,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,1,1,0,0,0,0]
 => [4,5,6,2,3,1,7] => ? = 84
[[],[[],[]],[],[]]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,1,0,0]
 => [6,5,3,2,4,1,7] => ? = 21
[[],[[[]]],[],[]]
 => [1,0,1,1,1,0,0,0,1,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,1,0,0]
 => [6,5,2,3,4,1,7] => ? = 42
[[],[[],[]],[[]]]
 => [1,0,1,1,0,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,1,0,0,1,1,0,0,0]
 => [5,6,3,2,4,1,7] => ? = 42
[[],[[[]]],[[]]]
 => [1,0,1,1,1,0,0,0,1,1,0,0]
 => [1,1,0,1,1,1,0,0,0,1,1,0,0,0]
 => [5,6,2,3,4,1,7] => ? = 84
[[],[[],[],[]],[]]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,1,0,0,1,0,0]
 => [6,4,3,2,5,1,7] => ? = 28
[[],[[],[[]]],[]]
 => [1,0,1,1,0,1,1,0,0,0,1,0]
 => [1,1,0,1,1,0,1,1,0,0,0,1,0,0]
 => [6,3,4,2,5,1,7] => ? = 56
[[],[[[]],[]],[]]
 => [1,0,1,1,1,0,0,1,0,0,1,0]
 => [1,1,0,1,1,1,0,0,1,0,0,1,0,0]
 => [6,4,2,3,5,1,7] => ? = 56
[[],[[[],[]]],[]]
 => [1,0,1,1,1,0,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,1,0,0,0,1,0,0]
 => [6,3,2,4,5,1,7] => ? = 84
[[],[[[[]]]],[]]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,1,0,1,1,1,1,0,0,0,0,1,0,0]
 => [6,2,3,4,5,1,7] => ? = 168
[[],[[],[],[],[]]]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,1,0,0,0]
 => [5,4,3,2,6,1,7] => ? = 35
[[],[[],[],[[]]]]
 => [1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,0,1,1,0,0,0,0]
 => [4,5,3,2,6,1,7] => ? = 70
[[],[[],[[]],[]]]
 => [1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,1,1,0,0,1,0,0,0]
 => [5,3,4,2,6,1,7] => ? = 70
[[],[[],[[],[]]]]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,1,0,0,0,0]
 => [4,3,5,2,6,1,7] => ? = 105
[[],[[],[[[]]]]]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,1,1,0,0,0,0,0]
 => [3,4,5,2,6,1,7] => ? = 210
[[],[[[]],[],[]]]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,1,0,0,0]
 => [5,4,2,3,6,1,7] => ? = 70
[[],[[[]],[[]]]]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,1,1,0,0,0,0]
 => [4,5,2,3,6,1,7] => ? = 140
[[],[[[],[]],[]]]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,1,0,0,1,0,0,0]
 => [5,3,2,4,6,1,7] => ? = 105
[[],[[[[]]],[]]]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,1,0,1,1,1,1,0,0,0,1,0,0,0]
 => [5,2,3,4,6,1,7] => ? = 210
[[],[[[],[],[]]]]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,1,0,0,0,0]
 => [4,3,2,5,6,1,7] => ? = 140
[[],[[[],[[]]]]]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,1,0,1,1,0,0,0,0,0]
 => [3,4,2,5,6,1,7] => ? = 280
[[],[[[[]],[]]]]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,1,0,1,1,1,1,0,0,1,0,0,0,0]
 => [4,2,3,5,6,1,7] => ? = 280
[[],[[[[],[]]]]]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,1,0,0,0,0,0]
 => [3,2,4,5,6,1,7] => ? = 420
[[],[[[[[]]]]]]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
 => [2,3,4,5,6,1,7] => ? = 840
[[[]],[],[],[],[]]
 => [1,1,0,0,1,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,1,0,0]
 => [6,5,4,3,1,2,7] => ? = 14
[[[]],[],[],[[]]]
 => [1,1,0,0,1,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,0,1,1,0,0,0]
 => [5,6,4,3,1,2,7] => ? = 28
[[[]],[],[[]],[]]
 => [1,1,0,0,1,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,1,1,0,0,1,0,0]
 => [6,4,5,3,1,2,7] => ? = 28
[[[]],[],[[],[]]]
 => [1,1,0,0,1,0,1,1,0,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,1,0,0,0]
 => [5,4,6,3,1,2,7] => ? = 42
[[[]],[],[[[]]]]
 => [1,1,0,0,1,0,1,1,1,0,0,0]
 => [1,1,1,0,0,1,0,1,1,1,0,0,0,0]
 => [4,5,6,3,1,2,7] => ? = 84
[[[]],[[]],[],[]]
 => [1,1,0,0,1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,1,0,0]
 => [6,5,3,4,1,2,7] => ? = 28
[[[]],[[]],[[]]]
 => [1,1,0,0,1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,1,1,0,0,0]
 => [5,6,3,4,1,2,7] => ? = 56
[[[]],[[],[]],[]]
 => [1,1,0,0,1,1,0,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,1,0,0,1,0,0]
 => [6,4,3,5,1,2,7] => ? = 42
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.