Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000413
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Mapping
St000413: Ordered trees ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[]]
 => 1
[[],[]]
 => 1
[[[]]]
 => 1
[[],[],[]]
 => 1
[[],[[]]]
 => 2
[[[]],[]]
 => 2
[[[],[]]]
 => 1
[[[[]]]]
 => 1
[[],[],[],[]]
 => 1
[[],[],[[]]]
 => 3
[[],[[]],[]]
 => 3
[[],[[],[]]]
 => 2
[[],[[[]]]]
 => 2
[[[]],[],[]]
 => 3
[[[]],[[]]]
 => 1
[[[],[]],[]]
 => 2
[[[[]]],[]]
 => 2
[[[],[],[]]]
 => 1
[[[],[[]]]]
 => 2
[[[[]],[]]]
 => 2
[[[[],[]]]]
 => 1
[[[[[]]]]]
 => 1
[[],[],[],[],[]]
 => 1
[[],[],[],[[]]]
 => 4
[[],[],[[]],[]]
 => 4
[[],[],[[],[]]]
 => 3
[[],[],[[[]]]]
 => 3
[[],[[]],[],[]]
 => 4
[[],[[]],[[]]]
 => 3
[[],[[],[]],[]]
 => 3
[[],[[[]]],[]]
 => 3
[[],[[],[],[]]]
 => 2
[[],[[],[[]]]]
 => 4
[[],[[[]],[]]]
 => 4
[[],[[[],[]]]]
 => 2
[[],[[[[]]]]]
 => 2
[[[]],[],[],[]]
 => 4
[[[]],[],[[]]]
 => 3
[[[]],[[]],[]]
 => 3
[[[]],[[],[]]]
 => 2
[[[]],[[[]]]]
 => 2
[[[],[]],[],[]]
 => 3
[[[[]]],[],[]]
 => 3
[[[],[]],[[]]]
 => 2
[[[[]]],[[]]]
 => 2
[[[],[],[]],[]]
 => 2
[[[],[[]]],[]]
 => 4
[[[[]],[]],[]]
 => 4
[[[[],[]]],[]]
 => 2
[[[[[]]]],[]]
 => 2
Description
The number of ordered trees with the same underlying unordered tree.
Matching statistic: St000282
Mapping
Mp00047: Ordered trees —to poset⟶ Posets
St000282: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[]]
 => ([(0,1)],2)
 => 1
[[],[]]
 => ([(0,2),(1,2)],3)
 => 1
[[[]]]
 => ([(0,2),(2,1)],3)
 => 1
[[],[],[]]
 => ([(0,3),(1,3),(2,3)],4)
 => 1
[[],[[]]]
 => ([(0,3),(1,2),(2,3)],4)
 => 2
[[[]],[]]
 => ([(0,3),(1,2),(2,3)],4)
 => 2
[[[],[]]]
 => ([(0,3),(1,3),(3,2)],4)
 => 1
[[[[]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 1
[[],[],[],[]]
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
[[],[],[[]]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
[[],[[]],[]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
[[],[[],[]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => 2
[[],[[[]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => 2
[[[]],[],[]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 3
[[[]],[[]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => 1
[[[],[]],[]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => 2
[[[[]]],[]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => 2
[[[],[],[]]]
 => ([(0,4),(1,4),(2,4),(4,3)],5)
 => 1
[[[],[[]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => 2
[[[[]],[]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => 2
[[[[],[]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => 1
[[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 1
[[],[],[],[],[]]
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1
[[],[],[],[[]]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => 4
[[],[],[[]],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => 4
[[],[],[[],[]]]
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 3
[[],[],[[[]]]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 3
[[],[[]],[],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => 4
[[],[[]],[[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => 3
[[],[[],[]],[]]
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 3
[[],[[[]]],[]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 3
[[],[[],[],[]]]
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => 2
[[],[[],[[]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => 4
[[],[[[]],[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => 4
[[],[[[],[]]]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => 2
[[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => 2
[[[]],[],[],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => 4
[[[]],[],[[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => 3
[[[]],[[]],[]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => 3
[[[]],[[],[]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => 2
[[[]],[[[]]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => 2
[[[],[]],[],[]]
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => 3
[[[[]]],[],[]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => 3
[[[],[]],[[]]]
 => ([(0,4),(1,4),(2,3),(3,5),(4,5)],6)
 => 2
[[[[]]],[[]]]
 => ([(0,3),(1,4),(2,5),(3,5),(4,2)],6)
 => 2
[[[],[],[]],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => 2
[[[],[[]]],[]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => 4
[[[[]],[]],[]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => 4
[[[[],[]]],[]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => 2
[[[[[]]]],[]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => 2
Description
The size of the preimage of the map 'to poset' from Ordered trees to Posets.