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Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000412
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(load all 3 compositions to match this statistic)
St000412: Binary trees ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[.,[.,.]]
=> 2
[[.,.],.]
=> 2
[.,[.,[.,.]]]
=> 4
[.,[[.,.],.]]
=> 4
[[.,.],[.,.]]
=> 1
[[.,[.,.]],.]
=> 4
[[[.,.],.],.]
=> 4
[.,[.,[.,[.,.]]]]
=> 8
[.,[.,[[.,.],.]]]
=> 8
[.,[[.,.],[.,.]]]
=> 2
[.,[[.,[.,.]],.]]
=> 8
[.,[[[.,.],.],.]]
=> 8
[[.,.],[.,[.,.]]]
=> 4
[[.,.],[[.,.],.]]
=> 4
[[.,[.,.]],[.,.]]
=> 4
[[[.,.],.],[.,.]]
=> 4
[[.,[.,[.,.]]],.]
=> 8
[[.,[[.,.],.]],.]
=> 8
[[[.,.],[.,.]],.]
=> 2
[[[.,[.,.]],.],.]
=> 8
[[[[.,.],.],.],.]
=> 8
[.,[.,[.,[.,[.,.]]]]]
=> 16
[.,[.,[.,[[.,.],.]]]]
=> 16
[.,[.,[[.,.],[.,.]]]]
=> 4
[.,[.,[[.,[.,.]],.]]]
=> 16
[.,[.,[[[.,.],.],.]]]
=> 16
[.,[[.,.],[.,[.,.]]]]
=> 8
[.,[[.,.],[[.,.],.]]]
=> 8
[.,[[.,[.,.]],[.,.]]]
=> 8
[.,[[[.,.],.],[.,.]]]
=> 8
[.,[[.,[.,[.,.]]],.]]
=> 16
[.,[[.,[[.,.],.]],.]]
=> 16
[.,[[[.,.],[.,.]],.]]
=> 4
[.,[[[.,[.,.]],.],.]]
=> 16
[.,[[[[.,.],.],.],.]]
=> 16
[[.,.],[.,[.,[.,.]]]]
=> 8
[[.,.],[.,[[.,.],.]]]
=> 8
[[.,.],[[.,.],[.,.]]]
=> 2
[[.,.],[[.,[.,.]],.]]
=> 8
[[.,.],[[[.,.],.],.]]
=> 8
[[.,[.,.]],[.,[.,.]]]
=> 4
[[.,[.,.]],[[.,.],.]]
=> 4
[[[.,.],.],[.,[.,.]]]
=> 4
[[[.,.],.],[[.,.],.]]
=> 4
[[.,[.,[.,.]]],[.,.]]
=> 8
[[.,[[.,.],.]],[.,.]]
=> 8
[[[.,.],[.,.]],[.,.]]
=> 2
[[[.,[.,.]],.],[.,.]]
=> 8
[[[[.,.],.],.],[.,.]]
=> 8
[[.,[.,[.,[.,.]]]],.]
=> 16
Description
The number of binary trees with the same underlying unordered tree.
Matching statistic: St000281
Mp00013: Binary trees —to poset⟶ Posets
St000281: Posets ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 75%
St000281: Posets ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 75%
Values
[.,[.,.]]
=> ([(0,1)],2)
=> 2
[[.,.],.]
=> ([(0,1)],2)
=> 2
[.,[.,[.,.]]]
=> ([(0,2),(2,1)],3)
=> 4
[.,[[.,.],.]]
=> ([(0,2),(2,1)],3)
=> 4
[[.,.],[.,.]]
=> ([(0,2),(1,2)],3)
=> 1
[[.,[.,.]],.]
=> ([(0,2),(2,1)],3)
=> 4
[[[.,.],.],.]
=> ([(0,2),(2,1)],3)
=> 4
[.,[.,[.,[.,.]]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 8
[.,[.,[[.,.],.]]]
=> ([(0,3),(2,1),(3,2)],4)
=> 8
[.,[[.,.],[.,.]]]
=> ([(0,3),(1,3),(3,2)],4)
=> 2
[.,[[.,[.,.]],.]]
=> ([(0,3),(2,1),(3,2)],4)
=> 8
[.,[[[.,.],.],.]]
=> ([(0,3),(2,1),(3,2)],4)
=> 8
[[.,.],[.,[.,.]]]
=> ([(0,3),(1,2),(2,3)],4)
=> 4
[[.,.],[[.,.],.]]
=> ([(0,3),(1,2),(2,3)],4)
=> 4
[[.,[.,.]],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> 4
[[[.,.],.],[.,.]]
=> ([(0,3),(1,2),(2,3)],4)
=> 4
[[.,[.,[.,.]]],.]
=> ([(0,3),(2,1),(3,2)],4)
=> 8
[[.,[[.,.],.]],.]
=> ([(0,3),(2,1),(3,2)],4)
=> 8
[[[.,.],[.,.]],.]
=> ([(0,3),(1,3),(3,2)],4)
=> 2
[[[.,[.,.]],.],.]
=> ([(0,3),(2,1),(3,2)],4)
=> 8
[[[[.,.],.],.],.]
=> ([(0,3),(2,1),(3,2)],4)
=> 8
[.,[.,[.,[.,[.,.]]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 16
[.,[.,[.,[[.,.],.]]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 16
[.,[.,[[.,.],[.,.]]]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> 4
[.,[.,[[.,[.,.]],.]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 16
[.,[.,[[[.,.],.],.]]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 16
[.,[[.,.],[.,[.,.]]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> 8
[.,[[.,.],[[.,.],.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> 8
[.,[[.,[.,.]],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> 8
[.,[[[.,.],.],[.,.]]]
=> ([(0,4),(1,2),(2,4),(4,3)],5)
=> 8
[.,[[.,[.,[.,.]]],.]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 16
[.,[[.,[[.,.],.]],.]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 16
[.,[[[.,.],[.,.]],.]]
=> ([(0,4),(1,4),(2,3),(4,2)],5)
=> 4
[.,[[[.,[.,.]],.],.]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 16
[.,[[[[.,.],.],.],.]]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 16
[[.,.],[.,[.,[.,.]]]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> 8
[[.,.],[.,[[.,.],.]]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> 8
[[.,.],[[.,.],[.,.]]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> 2
[[.,.],[[.,[.,.]],.]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> 8
[[.,.],[[[.,.],.],.]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> 8
[[.,[.,.]],[.,[.,.]]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> 4
[[.,[.,.]],[[.,.],.]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> 4
[[[.,.],.],[.,[.,.]]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> 4
[[[.,.],.],[[.,.],.]]
=> ([(0,3),(1,2),(2,4),(3,4)],5)
=> 4
[[.,[.,[.,.]]],[.,.]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> 8
[[.,[[.,.],.]],[.,.]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> 8
[[[.,.],[.,.]],[.,.]]
=> ([(0,4),(1,3),(2,3),(3,4)],5)
=> 2
[[[.,[.,.]],.],[.,.]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> 8
[[[[.,.],.],.],[.,.]]
=> ([(0,4),(1,2),(2,3),(3,4)],5)
=> 8
[[.,[.,[.,[.,.]]]],.]
=> ([(0,4),(2,3),(3,1),(4,2)],5)
=> 16
[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[.,[.,[.,[[.,.],.]]]]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[.,[.,[[.,[.,.]],.]]]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[.,[.,[[[.,.],.],.]]]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[.,[[.,.],[.,[.,.]]]]]]
=> ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 32
[.,[.,[.,[[.,.],[[.,.],.]]]]]
=> ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 32
[.,[.,[.,[[.,[.,.]],[.,.]]]]]
=> ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 32
[.,[.,[.,[[[.,.],.],[.,.]]]]]
=> ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 32
[.,[.,[.,[[.,[.,[.,.]]],.]]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[.,[[.,[[.,.],.]],.]]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[.,[[[.,[.,.]],.],.]]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[.,[[[[.,.],.],.],.]]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[[.,.],[.,[.,[.,.]]]]]]
=> ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
=> ? = 32
[.,[.,[[.,.],[.,[[.,.],.]]]]]
=> ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
=> ? = 32
[.,[.,[[.,.],[[.,[.,.]],.]]]]
=> ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
=> ? = 32
[.,[.,[[.,.],[[[.,.],.],.]]]]
=> ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
=> ? = 32
[.,[.,[[.,[.,.]],[.,[.,.]]]]]
=> ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
=> ? = 16
[.,[.,[[.,[.,.]],[[.,.],.]]]]
=> ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
=> ? = 16
[.,[.,[[[.,.],.],[.,[.,.]]]]]
=> ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
=> ? = 16
[.,[.,[[[.,.],.],[[.,.],.]]]]
=> ([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)
=> ? = 16
[.,[.,[[.,[.,[.,.]]],[.,.]]]]
=> ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
=> ? = 32
[.,[.,[[.,[[.,.],.]],[.,.]]]]
=> ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
=> ? = 32
[.,[.,[[[.,[.,.]],.],[.,.]]]]
=> ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
=> ? = 32
[.,[.,[[[[.,.],.],.],[.,.]]]]
=> ([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)
=> ? = 32
[.,[.,[[.,[.,[.,[.,.]]]],.]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[[.,[.,[[.,.],.]]],.]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[[.,[[.,[.,.]],.]],.]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[[.,[[[.,.],.],.]],.]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[[[.,.],[.,[.,.]]],.]]]
=> ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 32
[.,[.,[[[.,.],[[.,.],.]],.]]]
=> ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 32
[.,[.,[[[.,[.,.]],[.,.]],.]]]
=> ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 32
[.,[.,[[[[.,.],.],[.,.]],.]]]
=> ([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)
=> ? = 32
[.,[.,[[[.,[.,[.,.]]],.],.]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[[[.,[[.,.],.]],.],.]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[[[[.,[.,.]],.],.],.]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[.,[[[[[.,.],.],.],.],.]]]
=> ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
=> ? = 64
[.,[[.,.],[[.,.],[.,[.,.]]]]]
=> ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
=> ? = 16
[.,[[.,.],[[.,.],[[.,.],.]]]]
=> ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
=> ? = 16
[.,[[.,.],[[.,[.,.]],[.,.]]]]
=> ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
=> ? = 16
[.,[[.,.],[[[.,.],.],[.,.]]]]
=> ([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)
=> ? = 16
[.,[[.,[.,.]],[.,[.,[.,.]]]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 32
[.,[[.,[.,.]],[.,[[.,.],.]]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 32
[.,[[.,[.,.]],[[.,[.,.]],.]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 32
[.,[[.,[.,.]],[[[.,.],.],.]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 32
[.,[[[.,.],.],[.,[.,[.,.]]]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 32
[.,[[[.,.],.],[.,[[.,.],.]]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 32
[.,[[[.,.],.],[[.,[.,.]],.]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 32
[.,[[[.,.],.],[[[.,.],.],.]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 32
[.,[[.,[.,[.,.]]],[.,[.,.]]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 32
[.,[[.,[.,[.,.]]],[[.,.],.]]]
=> ([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)
=> ? = 32
Description
The size of the preimage of the map 'to poset' from Binary trees to Posets.
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