Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000417
(load all 2 compositions to match this statistic)
Mapping
Mp00139: Ordered trees —Zeilberger's Strahler bijection⟶ Binary trees
Mp00015: Binary trees —to ordered tree: right child = right brother⟶ Ordered trees
St000417: Ordered trees ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[],[]]
 => [.,[.,.]]
 => [[],[]]
 => 2
[[[]]]
 => [[.,.],.]
 => [[[]]]
 => 1
[[],[],[]]
 => [.,[.,[.,.]]]
 => [[],[],[]]
 => 6
[[],[[]]]
 => [.,[[.,.],.]]
 => [[],[[]]]
 => 1
[[[]],[]]
 => [[.,[.,.]],.]
 => [[[],[]]]
 => 2
[[[],[]]]
 => [[.,.],[.,.]]
 => [[[]],[]]
 => 1
[[[[]]]]
 => [[[.,.],.],.]
 => [[[[]]]]
 => 1
[[],[],[],[]]
 => [.,[.,[.,[.,.]]]]
 => [[],[],[],[]]
 => 24
[[],[],[[]]]
 => [.,[.,[[.,.],.]]]
 => [[],[],[[]]]
 => 2
[[],[[]],[]]
 => [.,[[.,[.,.]],.]]
 => [[],[[],[]]]
 => 2
[[],[[],[]]]
 => [.,[[.,.],[.,.]]]
 => [[],[[]],[]]
 => 2
[[],[[[]]]]
 => [.,[[[.,.],.],.]]
 => [[],[[[]]]]
 => 1
[[[]],[],[]]
 => [[.,[.,[.,.]]],.]
 => [[[],[],[]]]
 => 6
[[[]],[[]]]
 => [[.,[[.,.],.]],.]
 => [[[],[[]]]]
 => 1
[[[],[]],[]]
 => [[.,[.,.]],[.,.]]
 => [[[],[]],[]]
 => 2
[[[[]]],[]]
 => [[[.,[.,.]],.],.]
 => [[[[],[]]]]
 => 2
[[[],[],[]]]
 => [[.,.],[.,[.,.]]]
 => [[[]],[],[]]
 => 2
[[[],[[]]]]
 => [[.,.],[[.,.],.]]
 => [[[]],[[]]]
 => 2
[[[[]],[]]]
 => [[[.,.],.],[.,.]]
 => [[[[]]],[]]
 => 1
[[[[],[]]]]
 => [[[.,.],[.,.]],.]
 => [[[[]],[]]]
 => 1
[[[[[]]]]]
 => [[[[.,.],.],.],.]
 => [[[[[]]]]]
 => 1
[[],[],[],[],[]]
 => [.,[.,[.,[.,[.,.]]]]]
 => [[],[],[],[],[]]
 => 120
[[],[],[],[[]]]
 => [.,[.,[.,[[.,.],.]]]]
 => [[],[],[],[[]]]
 => 6
[[],[],[[]],[]]
 => [.,[.,[[.,[.,.]],.]]]
 => [[],[],[[],[]]]
 => 4
[[],[],[[],[]]]
 => [.,[.,[[.,.],[.,.]]]]
 => [[],[],[[]],[]]
 => 6
[[],[],[[[]]]]
 => [.,[.,[[[.,.],.],.]]]
 => [[],[],[[[]]]]
 => 2
[[],[[]],[],[]]
 => [.,[[.,[.,[.,.]]],.]]
 => [[],[[],[],[]]]
 => 6
[[],[[]],[[]]]
 => [.,[[.,[[.,.],.]],.]]
 => [[],[[],[[]]]]
 => 1
[[],[[],[]],[]]
 => [.,[[.,[.,.]],[.,.]]]
 => [[],[[],[]],[]]
 => 4
[[],[[[]]],[]]
 => [.,[[[.,[.,.]],.],.]]
 => [[],[[[],[]]]]
 => 2
[[],[[],[],[]]]
 => [.,[[.,.],[.,[.,.]]]]
 => [[],[[]],[],[]]
 => 6
[[],[[],[[]]]]
 => [.,[[.,.],[[.,.],.]]]
 => [[],[[]],[[]]]
 => 2
[[],[[[]],[]]]
 => [.,[[[.,.],.],[.,.]]]
 => [[],[[[]]],[]]
 => 2
[[],[[[],[]]]]
 => [.,[[[.,.],[.,.]],.]]
 => [[],[[[]],[]]]
 => 1
[[],[[[[]]]]]
 => [.,[[[[.,.],.],.],.]]
 => [[],[[[[]]]]]
 => 1
[[[]],[],[],[]]
 => [[.,[.,[.,[.,.]]]],.]
 => [[[],[],[],[]]]
 => 24
[[[]],[],[[]]]
 => [[.,[.,[[.,.],.]]],.]
 => [[[],[],[[]]]]
 => 2
[[[]],[[]],[]]
 => [[.,[[.,[.,.]],.]],.]
 => [[[],[[],[]]]]
 => 2
[[[]],[[],[]]]
 => [[.,.],[[.,.],[.,.]]]
 => [[[]],[[]],[]]
 => 2
[[[]],[[[]]]]
 => [[.,[[[.,.],.],.]],.]
 => [[[],[[[]]]]]
 => 1
[[[],[]],[],[]]
 => [[.,[.,.]],[.,[.,.]]]
 => [[[],[]],[],[]]
 => 4
[[[[]]],[],[]]
 => [[[.,[.,[.,.]]],.],.]
 => [[[[],[],[]]]]
 => 6
[[[],[]],[[]]]
 => [[.,[.,.]],[[.,.],.]]
 => [[[],[]],[[]]]
 => 2
[[[[]]],[[]]]
 => [[[.,[[.,.],.]],.],.]
 => [[[[],[[]]]]]
 => 1
[[[],[],[]],[]]
 => [[.,[.,[.,.]]],[.,.]]
 => [[[],[],[]],[]]
 => 6
[[[],[[]]],[]]
 => [[.,[[.,.],.]],[.,.]]
 => [[[],[[]]],[]]
 => 1
[[[[]],[]],[]]
 => [[[.,[.,.]],.],[.,.]]
 => [[[[],[]]],[]]
 => 2
[[[[],[]]],[]]
 => [[[.,[.,.]],[.,.]],.]
 => [[[[],[]],[]]]
 => 2
[[[[[]]]],[]]
 => [[[[.,[.,.]],.],.],.]
 => [[[[[],[]]]]]
 => 2
[[[],[],[],[]]]
 => [[.,.],[.,[.,[.,.]]]]
 => [[[]],[],[],[]]
 => 6
Description
The size of the automorphism group of the ordered tree.
Matching statistic: St000633
(load all 2 compositions to match this statistic)
Mapping
Mp00139: Ordered trees —Zeilberger's Strahler bijection⟶ Binary trees
Mp00014: Binary trees —to 132-avoiding permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St000633: 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)
 => 1
[[[]],[]]
 => [[.,[.,.]],.]
 => [2,1,3] => ([(0,2),(1,2)],3)
 => 2
[[[],[]]]
 => [[.,.],[.,.]]
 => [3,1,2] => ([(1,2)],3)
 => 1
[[[[]]]]
 => [[[.,.],.],.]
 => [1,2,3] => ([(0,2),(2,1)],3)
 => 1
[[],[],[],[]]
 => [.,[.,[.,[.,.]]]]
 => [4,3,2,1] => ([],4)
 => 24
[[],[],[[]]]
 => [.,[.,[[.,.],.]]]
 => [3,4,2,1] => ([(2,3)],4)
 => 2
[[],[[]],[]]
 => [.,[[.,[.,.]],.]]
 => [3,2,4,1] => ([(1,3),(2,3)],4)
 => 2
[[],[[],[]]]
 => [.,[[.,.],[.,.]]]
 => [4,2,3,1] => ([(2,3)],4)
 => 2
[[],[[[]]]]
 => [.,[[[.,.],.],.]]
 => [2,3,4,1] => ([(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
[[[],[]],[]]
 => [[.,[.,.]],[.,.]]
 => [4,2,1,3] => ([(1,3),(2,3)],4)
 => 2
[[[[]]],[]]
 => [[[.,[.,.]],.],.]
 => [2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => 2
[[[],[],[]]]
 => [[.,.],[.,[.,.]]]
 => [4,3,1,2] => ([(2,3)],4)
 => 2
[[[],[[]]]]
 => [[.,.],[[.,.],.]]
 => [3,4,1,2] => ([(0,3),(1,2)],4)
 => 2
[[[[]],[]]]
 => [[[.,.],.],[.,.]]
 => [4,1,2,3] => ([(1,2),(2,3)],4)
 => 1
[[[[],[]]]]
 => [[[.,.],[.,.]],.]
 => [3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
 => 1
[[[[[]]]]]
 => [[[[.,.],.],.],.]
 => [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
[[],[],[[]],[]]
 => [.,[.,[[.,[.,.]],.]]]
 => [4,3,5,2,1] => ([(2,4),(3,4)],5)
 => 4
[[],[],[[],[]]]
 => [.,[.,[[.,.],[.,.]]]]
 => [5,3,4,2,1] => ([(3,4)],5)
 => 6
[[],[],[[[]]]]
 => [.,[.,[[[.,.],.],.]]]
 => [3,4,5,2,1] => ([(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
[[],[[],[]],[]]
 => [.,[[.,[.,.]],[.,.]]]
 => [5,3,2,4,1] => ([(2,4),(3,4)],5)
 => 4
[[],[[[]]],[]]
 => [.,[[[.,[.,.]],.],.]]
 => [3,2,4,5,1] => ([(1,4),(2,4),(4,3)],5)
 => 2
[[],[[],[],[]]]
 => [.,[[.,.],[.,[.,.]]]]
 => [5,4,2,3,1] => ([(3,4)],5)
 => 6
[[],[[],[[]]]]
 => [.,[[.,.],[[.,.],.]]]
 => [4,5,2,3,1] => ([(1,4),(2,3)],5)
 => 2
[[],[[[]],[]]]
 => [.,[[[.,.],.],[.,.]]]
 => [5,2,3,4,1] => ([(2,3),(3,4)],5)
 => 2
[[],[[[],[]]]]
 => [.,[[[.,.],[.,.]],.]]
 => [4,2,3,5,1] => ([(1,4),(2,3),(3,4)],5)
 => 1
[[],[[[[]]]]]
 => [.,[[[[.,.],.],.],.]]
 => [2,3,4,5,1] => ([(1,4),(3,2),(4,3)],5)
 => 1
[[[]],[],[],[]]
 => [[.,[.,[.,[.,.]]]],.]
 => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 24
[[[]],[],[[]]]
 => [[.,[.,[[.,.],.]]],.]
 => [3,4,2,1,5] => ([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
[[[]],[[]],[]]
 => [[.,[[.,[.,.]],.]],.]
 => [3,2,4,1,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
 => 2
[[[]],[[],[]]]
 => [[.,.],[[.,.],[.,.]]]
 => [5,3,4,1,2] => ([(1,4),(2,3)],5)
 => 2
[[[]],[[[]]]]
 => [[.,[[[.,.],.],.]],.]
 => [2,3,4,1,5] => ([(0,4),(1,2),(2,3),(3,4)],5)
 => 1
[[[],[]],[],[]]
 => [[.,[.,.]],[.,[.,.]]]
 => [5,4,2,1,3] => ([(2,4),(3,4)],5)
 => 4
[[[[]]],[],[]]
 => [[[.,[.,[.,.]]],.],.]
 => [3,2,1,4,5] => ([(0,4),(1,4),(2,4),(4,3)],5)
 => 6
[[[],[]],[[]]]
 => [[.,[.,.]],[[.,.],.]]
 => [4,5,2,1,3] => ([(0,4),(1,4),(2,3)],5)
 => 2
[[[[]]],[[]]]
 => [[[.,[[.,.],.]],.],.]
 => [2,3,1,4,5] => ([(0,4),(1,2),(2,4),(4,3)],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
[[[[]],[]],[]]
 => [[[.,[.,.]],.],[.,.]]
 => [5,2,1,3,4] => ([(1,4),(2,4),(4,3)],5)
 => 2
[[[[],[]]],[]]
 => [[[.,[.,.]],[.,.]],.]
 => [4,2,1,3,5] => ([(0,4),(1,3),(2,3),(3,4)],5)
 => 2
[[[[[]]]],[]]
 => [[[[.,[.,.]],.],.],.]
 => [2,1,3,4,5] => ([(0,4),(1,4),(2,3),(4,2)],5)
 => 2
[[[],[],[],[]]]
 => [[.,.],[.,[.,[.,.]]]]
 => [5,4,3,1,2] => ([(3,4)],5)
 => 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.