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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
Mp00047: Ordered trees to posetPosets
St000282: Posets ⟶ ℤResult quality: 13% values known / values provided: 13%distinct values known / distinct values provided: 40%
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
[[],[[]],[[[]]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ? = 6
[[],[[[]]],[[]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ? = 6
[[],[[],[[[]]]]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ? = 4
[[],[[[]],[[]]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ? = 2
[[],[[[[]]],[]]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ? = 4
[[],[[[[[]]]]]]
=> ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
=> ? = 2
[[[]],[],[[[]]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ? = 6
[[[]],[[]],[[]]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7)
=> ? = 1
[[[]],[[[]]],[]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ? = 6
[[[]],[[],[[]]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ? = 4
[[[]],[[[]],[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ? = 4
[[[]],[[[[]]]]]
=> ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
=> ? = 2
[[[[]]],[],[[]]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ? = 6
[[[[]]],[[]],[]]
=> ([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ? = 6
[[[[]]],[[[]]]]
=> ([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)
=> ? = 1
[[[],[[]]],[[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ? = 4
[[[[]],[]],[[]]]
=> ([(0,5),(1,3),(2,4),(3,6),(4,5),(5,6)],7)
=> ? = 4
[[[[[]]]],[[]]]
=> ([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)
=> ? = 2
[[[],[[[]]]],[]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ? = 4
[[[[]],[[]]],[]]
=> ([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ? = 2
[[[[[]]],[]],[]]
=> ([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)
=> ? = 4
[[[[[[]]]]],[]]
=> ([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)
=> ? = 2
[[[],[[]],[[]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ? = 3
[[[],[[],[[]]]]]
=> ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
=> ? = 4
[[[],[[[]],[]]]]
=> ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
=> ? = 4
[[[[]],[],[[]]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ? = 3
[[[[]],[[]],[]]]
=> ([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ? = 3
[[[[]],[[[]]]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 2
[[[[[]]],[[]]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 2
[[[[],[[]]],[]]]
=> ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
=> ? = 4
[[[[[]],[]],[]]]
=> ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
=> ? = 4
[[[[],[[[]]]]]]
=> ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
=> ? = 2
[[[[[]],[[]]]]]
=> ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
=> ? = 1
[[[[[[]]],[]]]]
=> ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
=> ? = 2
[[[[[],[[]]]]]]
=> ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 2
[[[[[[]],[]]]]]
=> ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 2
[[[[[[[]]]]]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 1
[[],[],[],[],[],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
=> ? = 1
[[],[],[],[],[],[[]]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ? = 6
[[],[],[],[],[[]],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ? = 6
[[],[],[],[],[[],[]]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ? = 5
[[],[],[],[],[[[]]]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
=> ? = 5
[[],[],[],[[]],[],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
=> ? = 6
[[],[],[],[[]],[[]]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,7),(6,7)],8)
=> ? = 10
[[],[],[],[[],[]],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
=> ? = 5
[[],[],[],[[[]]],[]]
=> ([(0,7),(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
=> ? = 5
[[],[],[],[[],[],[]]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6),(6,7)],8)
=> ? = 4
[[],[],[],[[],[[]]]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
=> ? = 8
[[],[],[],[[[]],[]]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,5),(5,6),(6,7)],8)
=> ? = 8
[[],[],[],[[[],[]]]]
=> ([(0,7),(1,7),(2,7),(3,6),(4,6),(5,7),(6,5)],8)
=> ? = 4
Description
The size of the preimage of the map 'to poset' from Ordered trees to Posets.