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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000417
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(load all 3 compositions to match this statistic)
St000417: Ordered trees ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[]]
=> 1
[[],[]]
=> 2
[[[]]]
=> 1
[[],[],[]]
=> 6
[[],[[]]]
=> 1
[[[]],[]]
=> 1
[[[],[]]]
=> 2
[[[[]]]]
=> 1
[[],[],[],[]]
=> 24
[[],[],[[]]]
=> 2
[[],[[]],[]]
=> 2
[[],[[],[]]]
=> 2
[[],[[[]]]]
=> 1
[[[]],[],[]]
=> 2
[[[]],[[]]]
=> 2
[[[],[]],[]]
=> 2
[[[[]]],[]]
=> 1
[[[],[],[]]]
=> 6
[[[],[[]]]]
=> 1
[[[[]],[]]]
=> 1
[[[[],[]]]]
=> 2
[[[[[]]]]]
=> 1
[[],[],[],[],[]]
=> 120
[[],[],[],[[]]]
=> 6
[[],[],[[]],[]]
=> 6
[[],[],[[],[]]]
=> 4
[[],[],[[[]]]]
=> 2
[[],[[]],[],[]]
=> 6
[[],[[]],[[]]]
=> 2
[[],[[],[]],[]]
=> 4
[[],[[[]]],[]]
=> 2
[[],[[],[],[]]]
=> 6
[[],[[],[[]]]]
=> 1
[[],[[[]],[]]]
=> 1
[[],[[[],[]]]]
=> 2
[[],[[[[]]]]]
=> 1
[[[]],[],[],[]]
=> 6
[[[]],[],[[]]]
=> 2
[[[]],[[]],[]]
=> 2
[[[]],[[],[]]]
=> 2
[[[]],[[[]]]]
=> 1
[[[],[]],[],[]]
=> 4
[[[[]]],[],[]]
=> 2
[[[],[]],[[]]]
=> 2
[[[[]]],[[]]]
=> 1
[[[],[],[]],[]]
=> 6
[[[],[[]]],[]]
=> 1
[[[[]],[]],[]]
=> 1
[[[[],[]]],[]]
=> 2
[[[[[]]]],[]]
=> 1
Description
The size of the automorphism group of the ordered tree.
Matching statistic: St000633
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(load all 3 compositions to match this statistic)
Mp00050: Ordered trees —to binary tree: right brother = right child⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000633: Posets ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 75%
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000633: Posets ⟶ ℤResult quality: 39% ●values known / values provided: 39%●distinct values known / distinct values provided: 75%
Values
[[]]
=> [.,.]
=> [1] => ([],1)
=> ? = 1
[[],[]]
=> [.,[.,.]]
=> [2,1] => ([],2)
=> 2
[[[]]]
=> [[.,.],.]
=> [1,2] => ([(0,1)],2)
=> 1
[[],[],[]]
=> [.,[.,[.,.]]]
=> [3,2,1] => ([],3)
=> 6
[[],[[]]]
=> [.,[[.,.],.]]
=> [2,3,1] => ([(1,2)],3)
=> 1
[[[]],[]]
=> [[.,.],[.,.]]
=> [3,1,2] => ([(1,2)],3)
=> 1
[[[],[]]]
=> [[.,[.,.]],.]
=> [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)
=> 2
[[],[[]],[]]
=> [.,[[.,.],[.,.]]]
=> [4,2,3,1] => ([(2,3)],4)
=> 2
[[],[[],[]]]
=> [.,[[.,[.,.]],.]]
=> [3,2,4,1] => ([(1,3),(2,3)],4)
=> 2
[[],[[[]]]]
=> [.,[[[.,.],.],.]]
=> [2,3,4,1] => ([(1,2),(2,3)],4)
=> 1
[[[]],[],[]]
=> [[.,.],[.,[.,.]]]
=> [4,3,1,2] => ([(2,3)],4)
=> 2
[[[]],[[]]]
=> [[.,.],[[.,.],.]]
=> [3,4,1,2] => ([(0,3),(1,2)],4)
=> 2
[[[],[]],[]]
=> [[.,[.,.]],[.,.]]
=> [4,2,1,3] => ([(1,3),(2,3)],4)
=> 2
[[[[]]],[]]
=> [[[.,.],.],[.,.]]
=> [4,1,2,3] => ([(1,2),(2,3)],4)
=> 1
[[[],[],[]]]
=> [[.,[.,[.,.]]],.]
=> [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> 6
[[[],[[]]]]
=> [[.,[[.,.],.]],.]
=> [2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
=> 1
[[[[]],[]]]
=> [[[.,.],[.,.]],.]
=> [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
=> 1
[[[[],[]]]]
=> [[[.,[.,.]],.],.]
=> [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)
=> 6
[[],[],[[]],[]]
=> [.,[.,[[.,.],[.,.]]]]
=> [5,3,4,2,1] => ([(3,4)],5)
=> 6
[[],[],[[],[]]]
=> [.,[.,[[.,[.,.]],.]]]
=> [4,3,5,2,1] => ([(2,4),(3,4)],5)
=> 4
[[],[],[[[]]]]
=> [.,[.,[[[.,.],.],.]]]
=> [3,4,5,2,1] => ([(2,3),(3,4)],5)
=> 2
[[],[[]],[],[]]
=> [.,[[.,.],[.,[.,.]]]]
=> [5,4,2,3,1] => ([(3,4)],5)
=> 6
[[],[[]],[[]]]
=> [.,[[.,.],[[.,.],.]]]
=> [4,5,2,3,1] => ([(1,4),(2,3)],5)
=> 2
[[],[[],[]],[]]
=> [.,[[.,[.,.]],[.,.]]]
=> [5,3,2,4,1] => ([(2,4),(3,4)],5)
=> 4
[[],[[[]]],[]]
=> [.,[[[.,.],.],[.,.]]]
=> [5,2,3,4,1] => ([(2,3),(3,4)],5)
=> 2
[[],[[],[],[]]]
=> [.,[[.,[.,[.,.]]],.]]
=> [4,3,2,5,1] => ([(1,4),(2,4),(3,4)],5)
=> 6
[[],[[],[[]]]]
=> [.,[[.,[[.,.],.]],.]]
=> [3,4,2,5,1] => ([(1,4),(2,3),(3,4)],5)
=> 1
[[],[[[]],[]]]
=> [.,[[[.,.],[.,.]],.]]
=> [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
=> 1
[[],[[[],[]]]]
=> [.,[[[.,[.,.]],.],.]]
=> [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
=> 2
[[],[[[[]]]]]
=> [.,[[[[.,.],.],.],.]]
=> [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
=> 1
[[[]],[],[],[]]
=> [[.,.],[.,[.,[.,.]]]]
=> [5,4,3,1,2] => ([(3,4)],5)
=> 6
[[[]],[],[[]]]
=> [[.,.],[.,[[.,.],.]]]
=> [4,5,3,1,2] => ([(1,4),(2,3)],5)
=> 2
[[[]],[[]],[]]
=> [[.,.],[[.,.],[.,.]]]
=> [5,3,4,1,2] => ([(1,4),(2,3)],5)
=> 2
[[[]],[[],[]]]
=> [[.,.],[[.,[.,.]],.]]
=> [4,3,5,1,2] => ([(0,4),(1,4),(2,3)],5)
=> 2
[[[]],[[[]]]]
=> [[.,.],[[[.,.],.],.]]
=> [3,4,5,1,2] => ([(0,3),(1,4),(4,2)],5)
=> 1
[[[],[]],[],[]]
=> [[.,[.,.]],[.,[.,.]]]
=> [5,4,2,1,3] => ([(2,4),(3,4)],5)
=> 4
[[[[]]],[],[]]
=> [[[.,.],.],[.,[.,.]]]
=> [5,4,1,2,3] => ([(2,3),(3,4)],5)
=> 2
[[[],[]],[[]]]
=> [[.,[.,.]],[[.,.],.]]
=> [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
=> 2
[[[[]]],[[]]]
=> [[[.,.],.],[[.,.],.]]
=> [4,5,1,2,3] => ([(0,3),(1,4),(4,2)],5)
=> 1
[[[],[],[]],[]]
=> [[.,[.,[.,.]]],[.,.]]
=> [5,3,2,1,4] => ([(1,4),(2,4),(3,4)],5)
=> 6
[[[],[[]]],[]]
=> [[.,[[.,.],.]],[.,.]]
=> [5,2,3,1,4] => ([(1,4),(2,3),(3,4)],5)
=> 1
[[[[]],[]],[]]
=> [[[.,.],[.,.]],[.,.]]
=> [5,3,1,2,4] => ([(1,4),(2,3),(3,4)],5)
=> 1
[[[[],[]]],[]]
=> [[[.,[.,.]],.],[.,.]]
=> [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5)
=> 2
[[[[[]]]],[]]
=> [[[[.,.],.],.],[.,.]]
=> [5,1,2,3,4] => ([(1,4),(3,2),(4,3)],5)
=> 1
[[[],[],[],[]]]
=> [[.,[.,[.,[.,.]]]],.]
=> [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 24
[[],[],[],[[],[[]]]]
=> [.,[.,[.,[[.,[[.,.],.]],.]]]]
=> [5,6,4,7,3,2,1] => ([(3,6),(4,5),(5,6)],7)
=> ? = 6
[[],[],[],[[[]],[]]]
=> [.,[.,[.,[[[.,.],[.,.]],.]]]]
=> [6,4,5,7,3,2,1] => ([(3,6),(4,5),(5,6)],7)
=> ? = 6
[[],[],[[]],[[[]]]]
=> [.,[.,[[.,.],[[[.,.],.],.]]]]
=> [5,6,7,3,4,2,1] => ([(2,4),(3,5),(5,6)],7)
=> ? = 2
[[],[],[[[]]],[[]]]
=> [.,[.,[[[.,.],.],[[.,.],.]]]]
=> [6,7,3,4,5,2,1] => ([(2,4),(3,5),(5,6)],7)
=> ? = 2
[[],[],[[],[[]]],[]]
=> [.,[.,[[.,[[.,.],.]],[.,.]]]]
=> [7,4,5,3,6,2,1] => ([(3,6),(4,5),(5,6)],7)
=> ? = 6
[[],[],[[[]],[]],[]]
=> [.,[.,[[[.,.],[.,.]],[.,.]]]]
=> [7,5,3,4,6,2,1] => ([(3,6),(4,5),(5,6)],7)
=> ? = 6
[[],[],[[],[[[]]]]]
=> [.,[.,[[.,[[[.,.],.],.]],.]]]
=> [4,5,6,3,7,2,1] => ([(2,6),(3,4),(4,5),(5,6)],7)
=> ? = 2
[[],[],[[[]],[[]]]]
=> [.,[.,[[[.,.],[[.,.],.]],.]]]
=> [5,6,3,4,7,2,1] => ([(2,5),(3,4),(4,6),(5,6)],7)
=> ? = 4
[[],[],[[[[]]],[]]]
=> [.,[.,[[[[.,.],.],[.,.]],.]]]
=> [6,3,4,5,7,2,1] => ([(2,6),(3,4),(4,5),(5,6)],7)
=> ? = 2
[[],[],[[[],[[]]]]]
=> [.,[.,[[[.,[[.,.],.]],.],.]]]
=> [4,5,3,6,7,2,1] => ([(2,6),(3,4),(4,6),(6,5)],7)
=> ? = 2
[[],[],[[[[]],[]]]]
=> [.,[.,[[[[.,.],[.,.]],.],.]]]
=> [5,3,4,6,7,2,1] => ([(2,6),(3,4),(4,6),(6,5)],7)
=> ? = 2
[[],[],[[[[[]]]]]]
=> [.,[.,[[[[[.,.],.],.],.],.]]]
=> [3,4,5,6,7,2,1] => ([(2,6),(4,5),(5,3),(6,4)],7)
=> ? = 2
[[],[[]],[],[[[]]]]
=> [.,[[.,.],[.,[[[.,.],.],.]]]]
=> [5,6,7,4,2,3,1] => ([(2,4),(3,5),(5,6)],7)
=> ? = 2
[[],[[]],[[]],[[]]]
=> [.,[[.,.],[[.,.],[[.,.],.]]]]
=> [6,7,4,5,2,3,1] => ([(1,6),(2,5),(3,4)],7)
=> ? = 6
[[],[[]],[[[]]],[]]
=> [.,[[.,.],[[[.,.],.],[.,.]]]]
=> [7,4,5,6,2,3,1] => ([(2,4),(3,5),(5,6)],7)
=> ? = 2
[[],[[]],[[],[[]]]]
=> [.,[[.,.],[[.,[[.,.],.]],.]]]
=> [5,6,4,7,2,3,1] => ([(1,6),(2,4),(3,5),(5,6)],7)
=> ? = 1
[[],[[]],[[[]],[]]]
=> [.,[[.,.],[[[.,.],[.,.]],.]]]
=> [6,4,5,7,2,3,1] => ([(1,6),(2,4),(3,5),(5,6)],7)
=> ? = 1
[[],[[]],[[[[]]]]]
=> [.,[[.,.],[[[[.,.],.],.],.]]]
=> [4,5,6,7,2,3,1] => ([(1,6),(2,4),(5,3),(6,5)],7)
=> ? = 1
[[],[[[]]],[],[[]]]
=> [.,[[[.,.],.],[.,[[.,.],.]]]]
=> [6,7,5,2,3,4,1] => ([(2,4),(3,5),(5,6)],7)
=> ? = 2
[[],[[[]]],[[]],[]]
=> [.,[[[.,.],.],[[.,.],[.,.]]]]
=> [7,5,6,2,3,4,1] => ([(2,4),(3,5),(5,6)],7)
=> ? = 2
[[],[[[]]],[[[]]]]
=> [.,[[[.,.],.],[[[.,.],.],.]]]
=> [5,6,7,2,3,4,1] => ([(1,6),(2,5),(5,3),(6,4)],7)
=> ? = 2
[[],[[],[[]]],[],[]]
=> [.,[[.,[[.,.],.]],[.,[.,.]]]]
=> [7,6,3,4,2,5,1] => ([(3,6),(4,5),(5,6)],7)
=> ? = 6
[[],[[[]],[]],[],[]]
=> [.,[[[.,.],[.,.]],[.,[.,.]]]]
=> [7,6,4,2,3,5,1] => ([(3,6),(4,5),(5,6)],7)
=> ? = 6
[[],[[],[[]]],[[]]]
=> [.,[[.,[[.,.],.]],[[.,.],.]]]
=> [6,7,3,4,2,5,1] => ([(1,6),(2,4),(3,5),(5,6)],7)
=> ? = 1
[[],[[[]],[]],[[]]]
=> [.,[[[.,.],[.,.]],[[.,.],.]]]
=> [6,7,4,2,3,5,1] => ([(1,6),(2,4),(3,5),(5,6)],7)
=> ? = 1
[[],[[[[]]]],[[]]]
=> [.,[[[[.,.],.],.],[[.,.],.]]]
=> [6,7,2,3,4,5,1] => ([(1,6),(2,4),(5,3),(6,5)],7)
=> ? = 1
[[],[[],[[[]]]],[]]
=> [.,[[.,[[[.,.],.],.]],[.,.]]]
=> [7,3,4,5,2,6,1] => ([(2,6),(3,4),(4,5),(5,6)],7)
=> ? = 2
[[],[[[]],[[]]],[]]
=> [.,[[[.,.],[[.,.],.]],[.,.]]]
=> [7,4,5,2,3,6,1] => ([(2,5),(3,4),(4,6),(5,6)],7)
=> ? = 4
[[],[[[[]]],[]],[]]
=> [.,[[[[.,.],.],[.,.]],[.,.]]]
=> [7,5,2,3,4,6,1] => ([(2,6),(3,4),(4,5),(5,6)],7)
=> ? = 2
[[],[[[],[[]]]],[]]
=> [.,[[[.,[[.,.],.]],.],[.,.]]]
=> [7,3,4,2,5,6,1] => ([(2,6),(3,4),(4,6),(6,5)],7)
=> ? = 2
[[],[[[[]],[]]],[]]
=> [.,[[[[.,.],[.,.]],.],[.,.]]]
=> [7,4,2,3,5,6,1] => ([(2,6),(3,4),(4,6),(6,5)],7)
=> ? = 2
[[],[[[[[]]]]],[]]
=> [.,[[[[[.,.],.],.],.],[.,.]]]
=> [7,2,3,4,5,6,1] => ([(2,6),(4,5),(5,3),(6,4)],7)
=> ? = 2
[[],[[],[[]],[[]]]]
=> [.,[[.,[[.,.],[[.,.],.]]],.]]
=> [5,6,3,4,2,7,1] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ? = 2
[[],[[],[[],[[]]]]]
=> [.,[[.,[[.,[[.,.],.]],.]],.]]
=> [4,5,3,6,2,7,1] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
=> ? = 1
[[],[[],[[[]],[]]]]
=> [.,[[.,[[[.,.],[.,.]],.]],.]]
=> [5,3,4,6,2,7,1] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
=> ? = 1
[[],[[[]],[],[[]]]]
=> [.,[[[.,.],[.,[[.,.],.]]],.]]
=> [5,6,4,2,3,7,1] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ? = 2
[[],[[[]],[[]],[]]]
=> [.,[[[.,.],[[.,.],[.,.]]],.]]
=> [6,4,5,2,3,7,1] => ([(1,6),(2,5),(3,4),(4,6),(5,6)],7)
=> ? = 2
[[],[[[]],[[[]]]]]
=> [.,[[[.,.],[[[.,.],.],.]],.]]
=> [4,5,6,2,3,7,1] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ? = 1
[[],[[[[]]],[[]]]]
=> [.,[[[[.,.],.],[[.,.],.]],.]]
=> [5,6,2,3,4,7,1] => ([(1,3),(2,4),(3,5),(4,6),(5,6)],7)
=> ? = 1
[[],[[[],[[]]],[]]]
=> [.,[[[.,[[.,.],.]],[.,.]],.]]
=> [6,3,4,2,5,7,1] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
=> ? = 1
[[],[[[[]],[]],[]]]
=> [.,[[[[.,.],[.,.]],[.,.]],.]]
=> [6,4,2,3,5,7,1] => ([(1,6),(2,5),(3,4),(4,6),(6,5)],7)
=> ? = 1
[[],[[[],[[[]]]]]]
=> [.,[[[.,[[[.,.],.],.]],.],.]]
=> [3,4,5,2,6,7,1] => ([(1,6),(2,3),(3,5),(5,6),(6,4)],7)
=> ? = 1
[[],[[[[]],[[]]]]]
=> [.,[[[[.,.],[[.,.],.]],.],.]]
=> [4,5,2,3,6,7,1] => ([(1,4),(2,3),(3,6),(4,6),(6,5)],7)
=> ? = 2
[[],[[[[[]]],[]]]]
=> [.,[[[[[.,.],.],[.,.]],.],.]]
=> [5,2,3,4,6,7,1] => ([(1,6),(2,3),(3,5),(5,6),(6,4)],7)
=> ? = 1
[[],[[[[],[[]]]]]]
=> [.,[[[[.,[[.,.],.]],.],.],.]]
=> [3,4,2,5,6,7,1] => ([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
=> ? = 1
[[],[[[[[]],[]]]]]
=> [.,[[[[[.,.],[.,.]],.],.],.]]
=> [4,2,3,5,6,7,1] => ([(1,6),(2,3),(3,6),(4,5),(6,4)],7)
=> ? = 1
[[],[[[[[[]]]]]]]
=> [.,[[[[[[.,.],.],.],.],.],.]]
=> [2,3,4,5,6,7,1] => ([(1,6),(3,5),(4,3),(5,2),(6,4)],7)
=> ? = 1
[[[]],[],[],[[[]]]]
=> [[.,.],[.,[.,[[[.,.],.],.]]]]
=> [5,6,7,4,3,1,2] => ([(2,4),(3,5),(5,6)],7)
=> ? = 2
[[[]],[],[[]],[[]]]
=> [[.,.],[.,[[.,.],[[.,.],.]]]]
=> [6,7,4,5,3,1,2] => ([(1,6),(2,5),(3,4)],7)
=> ? = 6
Description
The size of the automorphism group of a poset.
A poset automorphism is a permutation of the elements of the poset preserving the order relation.
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