Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000568
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Mapping
Mp00049: Ordered trees —to binary tree: left brother = left child⟶ Binary trees
St000568: Binary 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
[[],[[]],[]]
 => [[[.,.],[.,.]],.]
 => 2
[[],[[],[]]]
 => [[.,.],[[.,.],.]]
 => 2
[[],[[[]]]]
 => [[.,.],[.,[.,.]]]
 => 1
[[[]],[],[]]
 => [[[.,[.,.]],.],.]
 => 2
[[[]],[[]]]
 => [[.,[.,.]],[.,.]]
 => 2
[[[],[]],[]]
 => [[.,[[.,.],.]],.]
 => 2
[[[[]]],[]]
 => [[.,[.,[.,.]]],.]
 => 2
[[[],[],[]]]
 => [.,[[[.,.],.],.]]
 => 2
[[[],[[]]]]
 => [.,[[.,.],[.,.]]]
 => 2
[[[[]],[]]]
 => [.,[[.,[.,.]],.]]
 => 2
[[[[],[]]]]
 => [.,[.,[[.,.],.]]]
 => 2
[[[[[]]]]]
 => [.,[.,[.,[.,.]]]]
 => 1
[[],[],[],[],[]]
 => [[[[[.,.],.],.],.],.]
 => 1
[[],[],[],[[]]]
 => [[[[.,.],.],.],[.,.]]
 => 1
[[],[],[[]],[]]
 => [[[[.,.],.],[.,.]],.]
 => 2
[[],[],[[],[]]]
 => [[[.,.],.],[[.,.],.]]
 => 2
[[],[],[[[]]]]
 => [[[.,.],.],[.,[.,.]]]
 => 1
[[],[[]],[],[]]
 => [[[[.,.],[.,.]],.],.]
 => 2
[[],[[]],[[]]]
 => [[[.,.],[.,.]],[.,.]]
 => 2
[[],[[],[]],[]]
 => [[[.,.],[[.,.],.]],.]
 => 2
[[],[[[]]],[]]
 => [[[.,.],[.,[.,.]]],.]
 => 2
[[],[[],[],[]]]
 => [[.,.],[[[.,.],.],.]]
 => 2
[[],[[],[[]]]]
 => [[.,.],[[.,.],[.,.]]]
 => 2
[[],[[[]],[]]]
 => [[.,.],[[.,[.,.]],.]]
 => 2
[[],[[[],[]]]]
 => [[.,.],[.,[[.,.],.]]]
 => 2
[[],[[[[]]]]]
 => [[.,.],[.,[.,[.,.]]]]
 => 1
[[[]],[],[],[]]
 => [[[[.,[.,.]],.],.],.]
 => 2
[[[]],[],[[]]]
 => [[[.,[.,.]],.],[.,.]]
 => 2
[[[]],[[]],[]]
 => [[[.,[.,.]],[.,.]],.]
 => 3
[[[]],[[],[]]]
 => [[.,[.,.]],[[.,.],.]]
 => 3
[[[]],[[[]]]]
 => [[.,[.,.]],[.,[.,.]]]
 => 2
[[[],[]],[],[]]
 => [[[.,[[.,.],.]],.],.]
 => 2
[[[[]]],[],[]]
 => [[[.,[.,[.,.]]],.],.]
 => 2
[[[],[]],[[]]]
 => [[.,[[.,.],.]],[.,.]]
 => 2
[[[[]]],[[]]]
 => [[.,[.,[.,.]]],[.,.]]
 => 2
[[[],[],[]],[]]
 => [[.,[[[.,.],.],.]],.]
 => 2
[[[],[[]]],[]]
 => [[.,[[.,.],[.,.]]],.]
 => 2
[[[[]],[]],[]]
 => [[.,[[.,[.,.]],.]],.]
 => 3
[[[[],[]]],[]]
 => [[.,[.,[[.,.],.]]],.]
 => 3
[[[[[]]]],[]]
 => [[.,[.,[.,[.,.]]]],.]
 => 2
[[[],[],[],[]]]
 => [.,[[[[.,.],.],.],.]]
 => 2
Description
The hook number of a binary tree. A hook of a binary tree is a vertex together with is left- and its right-most branch. Then there is a unique decomposition of the tree into hooks and the hook number is the number of hooks in this decomposition.