Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St000412
(load all 3 compositions to match this statistic)
Mapping
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
Mapping
Mp00013: Binary trees —to poset⟶ Posets
St000281: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
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
Description
The size of the preimage of the map 'to poset' from Binary trees to Posets.