Identifier
-
Mp00139:
Ordered trees
—Zeilberger's Strahler bijection⟶
Binary trees
St000396: Binary trees ⟶ ℤ
Values
[[]] => [.,.] => 1
[[],[]] => [.,[.,.]] => 1
[[[]]] => [[.,.],.] => 1
[[],[],[]] => [.,[.,[.,.]]] => 1
[[],[[]]] => [.,[[.,.],.]] => 1
[[[]],[]] => [[.,[.,.]],.] => 1
[[[],[]]] => [[.,.],[.,.]] => 2
[[[[]]]] => [[[.,.],.],.] => 1
[[],[],[],[]] => [.,[.,[.,[.,.]]]] => 1
[[],[],[[]]] => [.,[.,[[.,.],.]]] => 1
[[],[[]],[]] => [.,[[.,[.,.]],.]] => 1
[[],[[],[]]] => [.,[[.,.],[.,.]]] => 2
[[],[[[]]]] => [.,[[[.,.],.],.]] => 1
[[[]],[],[]] => [[.,[.,[.,.]]],.] => 1
[[[]],[[]]] => [[.,[[.,.],.]],.] => 1
[[[],[]],[]] => [[.,[.,.]],[.,.]] => 2
[[[[]]],[]] => [[[.,[.,.]],.],.] => 1
[[[],[],[]]] => [[.,.],[.,[.,.]]] => 2
[[[],[[]]]] => [[.,.],[[.,.],.]] => 2
[[[[]],[]]] => [[[.,.],.],[.,.]] => 2
[[[[],[]]]] => [[[.,.],[.,.]],.] => 2
[[[[[]]]]] => [[[[.,.],.],.],.] => 1
[[],[],[],[],[]] => [.,[.,[.,[.,[.,.]]]]] => 1
[[],[],[],[[]]] => [.,[.,[.,[[.,.],.]]]] => 1
[[],[],[[]],[]] => [.,[.,[[.,[.,.]],.]]] => 1
[[],[],[[],[]]] => [.,[.,[[.,.],[.,.]]]] => 2
[[],[],[[[]]]] => [.,[.,[[[.,.],.],.]]] => 1
[[],[[]],[],[]] => [.,[[.,[.,[.,.]]],.]] => 1
[[],[[]],[[]]] => [.,[[.,[[.,.],.]],.]] => 1
[[],[[],[]],[]] => [.,[[.,[.,.]],[.,.]]] => 2
[[],[[[]]],[]] => [.,[[[.,[.,.]],.],.]] => 1
[[],[[],[],[]]] => [.,[[.,.],[.,[.,.]]]] => 2
[[],[[],[[]]]] => [.,[[.,.],[[.,.],.]]] => 2
[[],[[[]],[]]] => [.,[[[.,.],.],[.,.]]] => 2
[[],[[[],[]]]] => [.,[[[.,.],[.,.]],.]] => 2
[[],[[[[]]]]] => [.,[[[[.,.],.],.],.]] => 1
[[[]],[],[],[]] => [[.,[.,[.,[.,.]]]],.] => 1
[[[]],[],[[]]] => [[.,[.,[[.,.],.]]],.] => 1
[[[]],[[]],[]] => [[.,[[.,[.,.]],.]],.] => 1
[[[]],[[],[]]] => [[.,.],[[.,.],[.,.]]] => 2
[[[]],[[[]]]] => [[.,[[[.,.],.],.]],.] => 1
[[[],[]],[],[]] => [[.,[.,.]],[.,[.,.]]] => 2
[[[[]]],[],[]] => [[[.,[.,[.,.]]],.],.] => 1
[[[],[]],[[]]] => [[.,[.,.]],[[.,.],.]] => 2
[[[[]]],[[]]] => [[[.,[[.,.],.]],.],.] => 1
[[[],[],[]],[]] => [[.,[.,[.,.]]],[.,.]] => 2
[[[],[[]]],[]] => [[.,[[.,.],.]],[.,.]] => 2
[[[[]],[]],[]] => [[[.,[.,.]],.],[.,.]] => 2
[[[[],[]]],[]] => [[[.,[.,.]],[.,.]],.] => 2
[[[[[]]]],[]] => [[[[.,[.,.]],.],.],.] => 1
[[[],[],[],[]]] => [[.,.],[.,[.,[.,.]]]] => 2
[[[],[],[[]]]] => [[.,.],[.,[[.,.],.]]] => 2
[[[],[[]],[]]] => [[.,.],[[.,[.,.]],.]] => 2
[[[],[[],[]]]] => [[.,[[.,.],[.,.]]],.] => 2
[[[],[[[]]]]] => [[.,.],[[[.,.],.],.]] => 2
[[[[]],[],[]]] => [[[.,.],.],[.,[.,.]]] => 2
[[[[]],[[]]]] => [[[.,.],.],[[.,.],.]] => 2
[[[[],[]],[]]] => [[[.,.],[.,.]],[.,.]] => 2
[[[[[]]],[]]] => [[[[.,.],.],.],[.,.]] => 2
[[[[],[],[]]]] => [[[.,.],[.,[.,.]]],.] => 2
[[[[],[[]]]]] => [[[.,.],[[.,.],.]],.] => 2
[[[[[]],[]]]] => [[[[.,.],.],[.,.]],.] => 2
[[[[[],[]]]]] => [[[[.,.],[.,.]],.],.] => 2
[[[[[[]]]]]] => [[[[[.,.],.],.],.],.] => 1
[[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,.]]]]]] => 1
[[],[],[],[],[[]]] => [.,[.,[.,[.,[[.,.],.]]]]] => 1
[[],[],[],[[]],[]] => [.,[.,[.,[[.,[.,.]],.]]]] => 1
[[],[],[],[[],[]]] => [.,[.,[.,[[.,.],[.,.]]]]] => 2
[[],[],[],[[[]]]] => [.,[.,[.,[[[.,.],.],.]]]] => 1
[[],[],[[]],[],[]] => [.,[.,[[.,[.,[.,.]]],.]]] => 1
[[],[],[[]],[[]]] => [.,[.,[[.,[[.,.],.]],.]]] => 1
[[],[],[[],[]],[]] => [.,[.,[[.,[.,.]],[.,.]]]] => 2
[[],[],[[[]]],[]] => [.,[.,[[[.,[.,.]],.],.]]] => 1
[[],[],[[],[],[]]] => [.,[.,[[.,.],[.,[.,.]]]]] => 2
[[],[],[[],[[]]]] => [.,[.,[[.,.],[[.,.],.]]]] => 2
[[],[],[[[]],[]]] => [.,[.,[[[.,.],.],[.,.]]]] => 2
[[],[],[[[],[]]]] => [.,[.,[[[.,.],[.,.]],.]]] => 2
[[],[],[[[[]]]]] => [.,[.,[[[[.,.],.],.],.]]] => 1
[[],[[]],[],[],[]] => [.,[[.,[.,[.,[.,.]]]],.]] => 1
[[],[[]],[],[[]]] => [.,[[.,[.,[[.,.],.]]],.]] => 1
[[],[[]],[[]],[]] => [.,[[.,[[.,[.,.]],.]],.]] => 1
[[],[[]],[[],[]]] => [.,[[.,.],[[.,.],[.,.]]]] => 2
[[],[[]],[[[]]]] => [.,[[.,[[[.,.],.],.]],.]] => 1
[[],[[],[]],[],[]] => [.,[[.,[.,.]],[.,[.,.]]]] => 2
[[],[[[]]],[],[]] => [.,[[[.,[.,[.,.]]],.],.]] => 1
[[],[[],[]],[[]]] => [.,[[.,[.,.]],[[.,.],.]]] => 2
[[],[[[]]],[[]]] => [.,[[[.,[[.,.],.]],.],.]] => 1
[[],[[],[],[]],[]] => [.,[[.,[.,[.,.]]],[.,.]]] => 2
[[],[[],[[]]],[]] => [.,[[.,[[.,.],.]],[.,.]]] => 2
[[],[[[]],[]],[]] => [.,[[[.,[.,.]],.],[.,.]]] => 2
[[],[[[],[]]],[]] => [.,[[[.,[.,.]],[.,.]],.]] => 2
[[],[[[[]]]],[]] => [.,[[[[.,[.,.]],.],.],.]] => 1
[[],[[],[],[],[]]] => [.,[[.,.],[.,[.,[.,.]]]]] => 2
[[],[[],[],[[]]]] => [.,[[.,.],[.,[[.,.],.]]]] => 2
[[],[[],[[]],[]]] => [.,[[.,.],[[.,[.,.]],.]]] => 2
[[],[[],[[],[]]]] => [.,[[.,[[.,.],[.,.]]],.]] => 2
[[],[[],[[[]]]]] => [.,[[.,.],[[[.,.],.],.]]] => 2
[[],[[[]],[],[]]] => [.,[[[.,.],.],[.,[.,.]]]] => 2
[[],[[[]],[[]]]] => [.,[[[.,.],.],[[.,.],.]]] => 2
[[],[[[],[]],[]]] => [.,[[[.,.],[.,.]],[.,.]]] => 2
[[],[[[[]]],[]]] => [.,[[[[.,.],.],.],[.,.]]] => 2
>>> Load all 1200 entries. <<<[[],[[[],[],[]]]] => [.,[[[.,.],[.,[.,.]]],.]] => 2
[[],[[[],[[]]]]] => [.,[[[.,.],[[.,.],.]],.]] => 2
[[],[[[[]],[]]]] => [.,[[[[.,.],.],[.,.]],.]] => 2
[[],[[[[],[]]]]] => [.,[[[[.,.],[.,.]],.],.]] => 2
[[],[[[[[]]]]]] => [.,[[[[[.,.],.],.],.],.]] => 1
[[[]],[],[],[],[]] => [[.,[.,[.,[.,[.,.]]]]],.] => 1
[[[]],[],[],[[]]] => [[.,[.,[.,[[.,.],.]]]],.] => 1
[[[]],[],[[]],[]] => [[.,[.,[[.,[.,.]],.]]],.] => 1
[[[]],[],[[],[]]] => [[.,.],[.,[[.,.],[.,.]]]] => 2
[[[]],[],[[[]]]] => [[.,[.,[[[.,.],.],.]]],.] => 1
[[[]],[[]],[],[]] => [[.,[[.,[.,[.,.]]],.]],.] => 1
[[[]],[[]],[[]]] => [[.,[[.,[[.,.],.]],.]],.] => 1
[[[]],[[],[]],[]] => [[.,.],[[.,[.,.]],[.,.]]] => 2
[[[]],[[[]]],[]] => [[.,[[[.,[.,.]],.],.]],.] => 1
[[[]],[[],[],[]]] => [[.,.],[[.,.],[.,[.,.]]]] => 2
[[[]],[[],[[]]]] => [[.,.],[[.,.],[[.,.],.]]] => 2
[[[]],[[[]],[]]] => [[.,.],[[[.,.],.],[.,.]]] => 2
[[[]],[[[],[]]]] => [[.,.],[[[.,.],[.,.]],.]] => 2
[[[]],[[[[]]]]] => [[.,[[[[.,.],.],.],.]],.] => 1
[[[],[]],[],[],[]] => [[.,[.,.]],[.,[.,[.,.]]]] => 2
[[[[]]],[],[],[]] => [[[.,[.,[.,[.,.]]]],.],.] => 1
[[[],[]],[],[[]]] => [[.,[.,.]],[.,[[.,.],.]]] => 2
[[[[]]],[],[[]]] => [[[.,[.,[[.,.],.]]],.],.] => 1
[[[],[]],[[]],[]] => [[.,[.,.]],[[.,[.,.]],.]] => 2
[[[[]]],[[]],[]] => [[[.,[[.,[.,.]],.]],.],.] => 1
[[[],[]],[[],[]]] => [[.,[.,.]],[[.,.],[.,.]]] => 2
[[[],[]],[[[]]]] => [[.,[.,.]],[[[.,.],.],.]] => 2
[[[[]]],[[],[]]] => [[[.,.],.],[[.,.],[.,.]]] => 2
[[[[]]],[[[]]]] => [[[.,[[[.,.],.],.]],.],.] => 1
[[[],[],[]],[],[]] => [[.,[.,[.,.]]],[.,[.,.]]] => 2
[[[],[[]]],[],[]] => [[.,[[.,.],.]],[.,[.,.]]] => 2
[[[[]],[]],[],[]] => [[[.,[.,.]],.],[.,[.,.]]] => 2
[[[[],[]]],[],[]] => [[[.,[.,.]],[.,[.,.]]],.] => 2
[[[[[]]]],[],[]] => [[[[.,[.,[.,.]]],.],.],.] => 1
[[[],[],[]],[[]]] => [[.,[.,[.,.]]],[[.,.],.]] => 2
[[[],[[]]],[[]]] => [[.,[[.,.],.]],[[.,.],.]] => 2
[[[[]],[]],[[]]] => [[[.,[.,.]],.],[[.,.],.]] => 2
[[[[],[]]],[[]]] => [[[.,[.,.]],[[.,.],.]],.] => 2
[[[[[]]]],[[]]] => [[[[.,[[.,.],.]],.],.],.] => 1
[[[],[],[],[]],[]] => [[.,[.,[.,[.,.]]]],[.,.]] => 2
[[[],[],[[]]],[]] => [[.,[.,[[.,.],.]]],[.,.]] => 2
[[[],[[]],[]],[]] => [[.,[[.,[.,.]],.]],[.,.]] => 2
[[[],[[],[]]],[]] => [[.,[[.,[.,.]],[.,.]]],.] => 2
[[[],[[[]]]],[]] => [[.,[[[.,.],.],.]],[.,.]] => 2
[[[[]],[],[]],[]] => [[[.,[.,[.,.]]],.],[.,.]] => 2
[[[[]],[[]]],[]] => [[[.,[[.,.],.]],.],[.,.]] => 2
[[[[],[]],[]],[]] => [[[.,[.,.]],[.,.]],[.,.]] => 2
[[[[[]]],[]],[]] => [[[[.,[.,.]],.],.],[.,.]] => 2
[[[[],[],[]]],[]] => [[[.,[.,[.,.]]],[.,.]],.] => 2
[[[[],[[]]]],[]] => [[[.,[[.,.],.]],[.,.]],.] => 2
[[[[[]],[]]],[]] => [[[[.,[.,.]],.],[.,.]],.] => 2
[[[[[],[]]]],[]] => [[[[.,[.,.]],[.,.]],.],.] => 2
[[[[[[]]]]],[]] => [[[[[.,[.,.]],.],.],.],.] => 1
[[[],[],[],[],[]]] => [[.,.],[.,[.,[.,[.,.]]]]] => 2
[[[],[],[],[[]]]] => [[.,.],[.,[.,[[.,.],.]]]] => 2
[[[],[],[[]],[]]] => [[.,.],[.,[[.,[.,.]],.]]] => 2
[[[],[],[[],[]]]] => [[.,[.,[[.,.],[.,.]]]],.] => 2
[[[],[],[[[]]]]] => [[.,.],[.,[[[.,.],.],.]]] => 2
[[[],[[]],[],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => 2
[[[],[[]],[[]]]] => [[.,.],[[.,[[.,.],.]],.]] => 2
[[[],[[],[]],[]]] => [[.,[[.,.],[.,.]]],[.,.]] => 2
[[[],[[[]]],[]]] => [[.,.],[[[.,[.,.]],.],.]] => 2
[[[],[[],[],[]]]] => [[.,[[.,.],[.,[.,.]]]],.] => 2
[[[],[[],[[]]]]] => [[.,[[.,.],[[.,.],.]]],.] => 2
[[[],[[[]],[]]]] => [[.,[[[.,.],.],[.,.]]],.] => 2
[[[],[[[],[]]]]] => [[.,[[[.,.],[.,.]],.]],.] => 2
[[[],[[[[]]]]]] => [[.,.],[[[[.,.],.],.],.]] => 2
[[[[]],[],[],[]]] => [[[.,.],.],[.,[.,[.,.]]]] => 2
[[[[]],[],[[]]]] => [[[.,.],.],[.,[[.,.],.]]] => 2
[[[[]],[[]],[]]] => [[[.,.],.],[[.,[.,.]],.]] => 2
[[[[]],[[],[]]]] => [[[.,.],[[.,.],[.,.]]],.] => 2
[[[[]],[[[]]]]] => [[[.,.],.],[[[.,.],.],.]] => 2
[[[[],[]],[],[]]] => [[[.,.],[.,.]],[.,[.,.]]] => 2
[[[[[]]],[],[]]] => [[[[.,.],.],.],[.,[.,.]]] => 2
[[[[],[]],[[]]]] => [[[.,.],[.,.]],[[.,.],.]] => 2
[[[[[]]],[[]]]] => [[[[.,.],.],.],[[.,.],.]] => 2
[[[[],[],[]],[]]] => [[[.,.],[.,[.,.]]],[.,.]] => 2
[[[[],[[]]],[]]] => [[[.,.],[[.,.],.]],[.,.]] => 2
[[[[[]],[]],[]]] => [[[[.,.],.],[.,.]],[.,.]] => 2
[[[[[],[]]],[]]] => [[[[.,.],[.,.]],.],[.,.]] => 2
[[[[[[]]]],[]]] => [[[[[.,.],.],.],.],[.,.]] => 2
[[[[],[],[],[]]]] => [[[.,.],[.,[.,[.,.]]]],.] => 2
[[[[],[],[[]]]]] => [[[.,.],[.,[[.,.],.]]],.] => 2
[[[[],[[]],[]]]] => [[[.,.],[[.,[.,.]],.]],.] => 2
[[[[],[[],[]]]]] => [[[.,[[.,.],[.,.]]],.],.] => 2
[[[[],[[[]]]]]] => [[[.,.],[[[.,.],.],.]],.] => 2
[[[[[]],[],[]]]] => [[[[.,.],.],[.,[.,.]]],.] => 2
[[[[[]],[[]]]]] => [[[[.,.],.],[[.,.],.]],.] => 2
[[[[[],[]],[]]]] => [[[[.,.],[.,.]],[.,.]],.] => 2
[[[[[[]]],[]]]] => [[[[[.,.],.],.],[.,.]],.] => 2
[[[[[],[],[]]]]] => [[[[.,.],[.,[.,.]]],.],.] => 2
[[[[[],[[]]]]]] => [[[[.,.],[[.,.],.]],.],.] => 2
[[[[[[]],[]]]]] => [[[[[.,.],.],[.,.]],.],.] => 2
[[[[[[],[]]]]]] => [[[[[.,.],[.,.]],.],.],.] => 2
[[[[[[[]]]]]]] => [[[[[[.,.],.],.],.],.],.] => 1
[[],[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,[.,.]]]]]]] => 1
[[],[],[],[],[],[[]]] => [.,[.,[.,[.,[.,[[.,.],.]]]]]] => 1
[[],[],[],[],[[]],[]] => [.,[.,[.,[.,[[.,[.,.]],.]]]]] => 1
[[],[],[],[],[[],[]]] => [.,[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[[],[],[],[],[[[]]]] => [.,[.,[.,[.,[[[.,.],.],.]]]]] => 1
[[],[],[],[[]],[],[]] => [.,[.,[.,[[.,[.,[.,.]]],.]]]] => 1
[[],[],[],[[]],[[]]] => [.,[.,[.,[[.,[[.,.],.]],.]]]] => 1
[[],[],[],[[],[]],[]] => [.,[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[[],[],[],[[[]]],[]] => [.,[.,[.,[[[.,[.,.]],.],.]]]] => 1
[[],[],[],[[],[],[]]] => [.,[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[[],[],[],[[],[[]]]] => [.,[.,[.,[[.,.],[[.,.],.]]]]] => 2
[[],[],[],[[[]],[]]] => [.,[.,[.,[[[.,.],.],[.,.]]]]] => 2
[[],[],[],[[[],[]]]] => [.,[.,[.,[[[.,.],[.,.]],.]]]] => 2
[[],[],[],[[[[]]]]] => [.,[.,[.,[[[[.,.],.],.],.]]]] => 1
[[],[],[[]],[],[],[]] => [.,[.,[[.,[.,[.,[.,.]]]],.]]] => 1
[[],[],[[]],[],[[]]] => [.,[.,[[.,[.,[[.,.],.]]],.]]] => 1
[[],[],[[]],[[]],[]] => [.,[.,[[.,[[.,[.,.]],.]],.]]] => 1
[[],[],[[]],[[],[]]] => [.,[.,[[.,.],[[.,.],[.,.]]]]] => 2
[[],[],[[]],[[[]]]] => [.,[.,[[.,[[[.,.],.],.]],.]]] => 1
[[],[],[[],[]],[],[]] => [.,[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[[],[],[[[]]],[],[]] => [.,[.,[[[.,[.,[.,.]]],.],.]]] => 1
[[],[],[[],[]],[[]]] => [.,[.,[[.,[.,.]],[[.,.],.]]]] => 2
[[],[],[[[]]],[[]]] => [.,[.,[[[.,[[.,.],.]],.],.]]] => 1
[[],[],[[],[],[]],[]] => [.,[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[[],[],[[],[[]]],[]] => [.,[.,[[.,[[.,.],.]],[.,.]]]] => 2
[[],[],[[[]],[]],[]] => [.,[.,[[[.,[.,.]],.],[.,.]]]] => 2
[[],[],[[[],[]]],[]] => [.,[.,[[[.,[.,.]],[.,.]],.]]] => 2
[[],[],[[[[]]]],[]] => [.,[.,[[[[.,[.,.]],.],.],.]]] => 1
[[],[],[[],[],[],[]]] => [.,[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[[],[],[[],[],[[]]]] => [.,[.,[[.,.],[.,[[.,.],.]]]]] => 2
[[],[],[[],[[]],[]]] => [.,[.,[[.,.],[[.,[.,.]],.]]]] => 2
[[],[],[[],[[],[]]]] => [.,[.,[[.,[[.,.],[.,.]]],.]]] => 2
[[],[],[[],[[[]]]]] => [.,[.,[[.,.],[[[.,.],.],.]]]] => 2
[[],[],[[[]],[],[]]] => [.,[.,[[[.,.],.],[.,[.,.]]]]] => 2
[[],[],[[[]],[[]]]] => [.,[.,[[[.,.],.],[[.,.],.]]]] => 2
[[],[],[[[],[]],[]]] => [.,[.,[[[.,.],[.,.]],[.,.]]]] => 2
[[],[],[[[[]]],[]]] => [.,[.,[[[[.,.],.],.],[.,.]]]] => 2
[[],[],[[[],[],[]]]] => [.,[.,[[[.,.],[.,[.,.]]],.]]] => 2
[[],[],[[[],[[]]]]] => [.,[.,[[[.,.],[[.,.],.]],.]]] => 2
[[],[],[[[[]],[]]]] => [.,[.,[[[[.,.],.],[.,.]],.]]] => 2
[[],[],[[[[],[]]]]] => [.,[.,[[[[.,.],[.,.]],.],.]]] => 2
[[],[],[[[[[]]]]]] => [.,[.,[[[[[.,.],.],.],.],.]]] => 1
[[],[[]],[],[],[],[]] => [.,[[.,[.,[.,[.,[.,.]]]]],.]] => 1
[[],[[]],[],[],[[]]] => [.,[[.,[.,[.,[[.,.],.]]]],.]] => 1
[[],[[]],[],[[]],[]] => [.,[[.,[.,[[.,[.,.]],.]]],.]] => 1
[[],[[]],[],[[],[]]] => [.,[[.,.],[.,[[.,.],[.,.]]]]] => 2
[[],[[]],[],[[[]]]] => [.,[[.,[.,[[[.,.],.],.]]],.]] => 1
[[],[[]],[[]],[],[]] => [.,[[.,[[.,[.,[.,.]]],.]],.]] => 1
[[],[[]],[[]],[[]]] => [.,[[.,[[.,[[.,.],.]],.]],.]] => 1
[[],[[]],[[],[]],[]] => [.,[[.,.],[[.,[.,.]],[.,.]]]] => 2
[[],[[]],[[[]]],[]] => [.,[[.,[[[.,[.,.]],.],.]],.]] => 1
[[],[[]],[[],[],[]]] => [.,[[.,.],[[.,.],[.,[.,.]]]]] => 2
[[],[[]],[[],[[]]]] => [.,[[.,.],[[.,.],[[.,.],.]]]] => 2
[[],[[]],[[[]],[]]] => [.,[[.,.],[[[.,.],.],[.,.]]]] => 2
[[],[[]],[[[],[]]]] => [.,[[.,.],[[[.,.],[.,.]],.]]] => 2
[[],[[]],[[[[]]]]] => [.,[[.,[[[[.,.],.],.],.]],.]] => 1
[[],[[],[]],[],[],[]] => [.,[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[[],[[[]]],[],[],[]] => [.,[[[.,[.,[.,[.,.]]]],.],.]] => 1
[[],[[],[]],[],[[]]] => [.,[[.,[.,.]],[.,[[.,.],.]]]] => 2
[[],[[[]]],[],[[]]] => [.,[[[.,[.,[[.,.],.]]],.],.]] => 1
[[],[[],[]],[[]],[]] => [.,[[.,[.,.]],[[.,[.,.]],.]]] => 2
[[],[[[]]],[[]],[]] => [.,[[[.,[[.,[.,.]],.]],.],.]] => 1
[[],[[],[]],[[],[]]] => [.,[[.,[.,.]],[[.,.],[.,.]]]] => 2
[[],[[],[]],[[[]]]] => [.,[[.,[.,.]],[[[.,.],.],.]]] => 2
[[],[[[]]],[[],[]]] => [.,[[[.,.],.],[[.,.],[.,.]]]] => 2
[[],[[[]]],[[[]]]] => [.,[[[.,[[[.,.],.],.]],.],.]] => 1
[[],[[],[],[]],[],[]] => [.,[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[[],[[],[[]]],[],[]] => [.,[[.,[[.,.],.]],[.,[.,.]]]] => 2
[[],[[[]],[]],[],[]] => [.,[[[.,[.,.]],.],[.,[.,.]]]] => 2
[[],[[[],[]]],[],[]] => [.,[[[.,[.,.]],[.,[.,.]]],.]] => 2
[[],[[[[]]]],[],[]] => [.,[[[[.,[.,[.,.]]],.],.],.]] => 1
[[],[[],[],[]],[[]]] => [.,[[.,[.,[.,.]]],[[.,.],.]]] => 2
[[],[[],[[]]],[[]]] => [.,[[.,[[.,.],.]],[[.,.],.]]] => 2
[[],[[[]],[]],[[]]] => [.,[[[.,[.,.]],.],[[.,.],.]]] => 2
[[],[[[],[]]],[[]]] => [.,[[[.,[.,.]],[[.,.],.]],.]] => 2
[[],[[[[]]]],[[]]] => [.,[[[[.,[[.,.],.]],.],.],.]] => 1
[[],[[],[],[],[]],[]] => [.,[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[[],[[],[],[[]]],[]] => [.,[[.,[.,[[.,.],.]]],[.,.]]] => 2
[[],[[],[[]],[]],[]] => [.,[[.,[[.,[.,.]],.]],[.,.]]] => 2
[[],[[],[[],[]]],[]] => [.,[[.,[[.,[.,.]],[.,.]]],.]] => 2
[[],[[],[[[]]]],[]] => [.,[[.,[[[.,.],.],.]],[.,.]]] => 2
[[],[[[]],[],[]],[]] => [.,[[[.,[.,[.,.]]],.],[.,.]]] => 2
[[],[[[]],[[]]],[]] => [.,[[[.,[[.,.],.]],.],[.,.]]] => 2
[[],[[[],[]],[]],[]] => [.,[[[.,[.,.]],[.,.]],[.,.]]] => 2
[[],[[[[]]],[]],[]] => [.,[[[[.,[.,.]],.],.],[.,.]]] => 2
[[],[[[],[],[]]],[]] => [.,[[[.,[.,[.,.]]],[.,.]],.]] => 2
[[],[[[],[[]]]],[]] => [.,[[[.,[[.,.],.]],[.,.]],.]] => 2
[[],[[[[]],[]]],[]] => [.,[[[[.,[.,.]],.],[.,.]],.]] => 2
[[],[[[[],[]]]],[]] => [.,[[[[.,[.,.]],[.,.]],.],.]] => 2
[[],[[[[[]]]]],[]] => [.,[[[[[.,[.,.]],.],.],.],.]] => 1
[[],[[],[],[],[],[]]] => [.,[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[[],[[],[],[],[[]]]] => [.,[[.,.],[.,[.,[[.,.],.]]]]] => 2
[[],[[],[],[[]],[]]] => [.,[[.,.],[.,[[.,[.,.]],.]]]] => 2
[[],[[],[],[[],[]]]] => [.,[[.,[.,[[.,.],[.,.]]]],.]] => 2
[[],[[],[],[[[]]]]] => [.,[[.,.],[.,[[[.,.],.],.]]]] => 2
[[],[[],[[]],[],[]]] => [.,[[.,.],[[.,[.,[.,.]]],.]]] => 2
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[[],[[[],[[[],[]]]]]] => [.,[[[.,[[[.,.],[.,.]],.]],.],.]] => 2
[[],[[[],[[[[]]]]]]] => [.,[[[.,.],[[[[.,.],.],.],.]],.]] => 2
[[],[[[[]],[],[],[]]]] => [.,[[[[.,.],.],[.,[.,[.,.]]]],.]] => 2
[[],[[[[]],[],[[]]]]] => [.,[[[[.,.],.],[.,[[.,.],.]]],.]] => 2
[[],[[[[]],[[]],[]]]] => [.,[[[[.,.],.],[[.,[.,.]],.]],.]] => 2
[[],[[[[]],[[],[]]]]] => [.,[[[[.,.],[[.,.],[.,.]]],.],.]] => 2
[[],[[[[]],[[[]]]]]] => [.,[[[[.,.],.],[[[.,.],.],.]],.]] => 2
[[],[[[[],[]],[],[]]]] => [.,[[[[.,.],[.,.]],[.,[.,.]]],.]] => 2
[[],[[[[[]]],[],[]]]] => [.,[[[[[.,.],.],.],[.,[.,.]]],.]] => 2
[[],[[[[],[]],[[]]]]] => [.,[[[[.,.],[.,.]],[[.,.],.]],.]] => 2
[[],[[[[[]]],[[]]]]] => [.,[[[[[.,.],.],.],[[.,.],.]],.]] => 2
[[],[[[[],[],[]],[]]]] => [.,[[[[.,.],[.,[.,.]]],[.,.]],.]] => 2
[[],[[[[],[[]]],[]]]] => [.,[[[[.,.],[[.,.],.]],[.,.]],.]] => 2
[[],[[[[[]],[]],[]]]] => [.,[[[[[.,.],.],[.,.]],[.,.]],.]] => 2
[[],[[[[[],[]]],[]]]] => [.,[[[[[.,.],[.,.]],.],[.,.]],.]] => 2
[[],[[[[[[]]]],[]]]] => [.,[[[[[[.,.],.],.],.],[.,.]],.]] => 2
[[],[[[[],[],[],[]]]]] => [.,[[[[.,.],[.,[.,[.,.]]]],.],.]] => 2
[[],[[[[],[],[[]]]]]] => [.,[[[[.,.],[.,[[.,.],.]]],.],.]] => 2
[[],[[[[],[[]],[]]]]] => [.,[[[[.,.],[[.,[.,.]],.]],.],.]] => 2
[[],[[[[],[[],[]]]]]] => [.,[[[[.,[[.,.],[.,.]]],.],.],.]] => 2
[[],[[[[],[[[]]]]]]] => [.,[[[[.,.],[[[.,.],.],.]],.],.]] => 2
[[],[[[[[]],[],[]]]]] => [.,[[[[[.,.],.],[.,[.,.]]],.],.]] => 2
[[],[[[[[]],[[]]]]]] => [.,[[[[[.,.],.],[[.,.],.]],.],.]] => 2
[[],[[[[[],[]],[]]]]] => [.,[[[[[.,.],[.,.]],[.,.]],.],.]] => 2
[[],[[[[[[]]],[]]]]] => [.,[[[[[[.,.],.],.],[.,.]],.],.]] => 2
[[],[[[[[],[],[]]]]]] => [.,[[[[[.,.],[.,[.,.]]],.],.],.]] => 2
[[],[[[[[],[[]]]]]]] => [.,[[[[[.,.],[[.,.],.]],.],.],.]] => 2
[[],[[[[[[]],[]]]]]] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => 2
[[],[[[[[[],[]]]]]]] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => 2
[[],[[[[[[[]]]]]]]] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => 1
[[[]],[],[],[],[[],[]]] => [[.,.],[.,[.,[.,[[.,.],[.,.]]]]]] => 2
[[[]],[],[],[[],[]],[]] => [[.,.],[.,[.,[[.,[.,.]],[.,.]]]]] => 2
[[[]],[],[],[[],[],[]]] => [[.,.],[.,[.,[[.,.],[.,[.,.]]]]]] => 2
[[[]],[],[],[[],[[]]]] => [[.,.],[.,[.,[[.,.],[[.,.],.]]]]] => 2
[[[]],[],[],[[[]],[]]] => [[.,.],[.,[.,[[[.,.],.],[.,.]]]]] => 2
[[[]],[],[],[[[],[]]]] => [[.,.],[.,[.,[[[.,.],[.,.]],.]]]] => 2
[[[]],[],[[]],[[],[]]] => [[.,.],[.,[[.,.],[[.,.],[.,.]]]]] => 2
[[[]],[],[[],[]],[],[]] => [[.,.],[.,[[.,[.,.]],[.,[.,.]]]]] => 2
[[[]],[],[[],[]],[[]]] => [[.,.],[.,[[.,[.,.]],[[.,.],.]]]] => 2
[[[]],[],[[],[],[]],[]] => [[.,.],[.,[[.,[.,[.,.]]],[.,.]]]] => 2
[[[]],[],[[],[[]]],[]] => [[.,.],[.,[[.,[[.,.],.]],[.,.]]]] => 2
[[[]],[],[[[]],[]],[]] => [[.,.],[.,[[[.,[.,.]],.],[.,.]]]] => 2
[[[]],[],[[[],[]]],[]] => [[.,.],[.,[[[.,[.,.]],[.,.]],.]]] => 2
[[[]],[],[[],[],[],[]]] => [[.,.],[.,[[.,.],[.,[.,[.,.]]]]]] => 2
[[[]],[],[[],[],[[]]]] => [[.,.],[.,[[.,.],[.,[[.,.],.]]]]] => 2
[[[]],[],[[],[[]],[]]] => [[.,.],[.,[[.,.],[[.,[.,.]],.]]]] => 2
[[[]],[],[[],[[],[]]]] => [[.,.],[.,[[.,[[.,.],[.,.]]],.]]] => 2
[[[]],[],[[],[[[]]]]] => [[.,.],[.,[[.,.],[[[.,.],.],.]]]] => 2
[[[]],[],[[[]],[],[]]] => [[.,.],[.,[[[.,.],.],[.,[.,.]]]]] => 2
[[[]],[],[[[]],[[]]]] => [[.,.],[.,[[[.,.],.],[[.,.],.]]]] => 2
[[[]],[],[[[],[]],[]]] => [[.,.],[.,[[[.,.],[.,.]],[.,.]]]] => 2
[[[]],[],[[[[]]],[]]] => [[.,.],[.,[[[[.,.],.],.],[.,.]]]] => 2
[[[]],[],[[[],[],[]]]] => [[.,.],[.,[[[.,.],[.,[.,.]]],.]]] => 2
[[[]],[],[[[],[[]]]]] => [[.,.],[.,[[[.,.],[[.,.],.]],.]]] => 2
[[[]],[],[[[[]],[]]]] => [[.,.],[.,[[[[.,.],.],[.,.]],.]]] => 2
[[[]],[],[[[[],[]]]]] => [[.,.],[.,[[[[.,.],[.,.]],.],.]]] => 2
[[[]],[[]],[],[[],[]]] => [[.,.],[[.,.],[.,[[.,.],[.,.]]]]] => 2
[[[]],[[]],[[],[]],[]] => [[.,.],[[.,.],[[.,[.,.]],[.,.]]]] => 2
[[[]],[[]],[[],[],[]]] => [[.,.],[[.,.],[[.,.],[.,[.,.]]]]] => 2
[[[]],[[]],[[],[[]]]] => [[.,.],[[.,.],[[.,.],[[.,.],.]]]] => 2
[[[]],[[]],[[[]],[]]] => [[.,.],[[.,.],[[[.,.],.],[.,.]]]] => 2
[[[]],[[]],[[[],[]]]] => [[.,.],[[.,.],[[[.,.],[.,.]],.]]] => 2
[[[]],[[],[]],[],[],[]] => [[.,.],[[.,[.,.]],[.,[.,[.,.]]]]] => 2
[[[]],[[],[]],[],[[]]] => [[.,.],[[.,[.,.]],[.,[[.,.],.]]]] => 2
[[[]],[[],[]],[[]],[]] => [[.,.],[[.,[.,.]],[[.,[.,.]],.]]] => 2
[[[]],[[],[]],[[],[]]] => [[.,.],[[.,[.,.]],[[.,.],[.,.]]]] => 2
[[[]],[[],[]],[[[]]]] => [[.,.],[[.,[.,.]],[[[.,.],.],.]]] => 2
[[[]],[[[]]],[[],[]]] => [[.,.],[[[.,.],.],[[.,.],[.,.]]]] => 2
[[[]],[[],[],[]],[],[]] => [[.,.],[[.,[.,[.,.]]],[.,[.,.]]]] => 2
[[[]],[[],[[]]],[],[]] => [[.,.],[[.,[[.,.],.]],[.,[.,.]]]] => 2
[[[]],[[[]],[]],[],[]] => [[.,.],[[[.,[.,.]],.],[.,[.,.]]]] => 2
[[[]],[[[],[]]],[],[]] => [[.,.],[[[.,[.,.]],[.,[.,.]]],.]] => 2
[[[]],[[],[],[]],[[]]] => [[.,.],[[.,[.,[.,.]]],[[.,.],.]]] => 2
[[[]],[[],[[]]],[[]]] => [[.,.],[[.,[[.,.],.]],[[.,.],.]]] => 2
[[[]],[[[]],[]],[[]]] => [[.,.],[[[.,[.,.]],.],[[.,.],.]]] => 2
[[[]],[[[],[]]],[[]]] => [[.,.],[[[.,[.,.]],[[.,.],.]],.]] => 2
[[[]],[[],[],[],[]],[]] => [[.,.],[[.,[.,[.,[.,.]]]],[.,.]]] => 2
[[[]],[[],[],[[]]],[]] => [[.,.],[[.,[.,[[.,.],.]]],[.,.]]] => 2
[[[]],[[],[[]],[]],[]] => [[.,.],[[.,[[.,[.,.]],.]],[.,.]]] => 2
[[[]],[[],[[],[]]],[]] => [[.,.],[[.,[[.,[.,.]],[.,.]]],.]] => 2
[[[]],[[],[[[]]]],[]] => [[.,.],[[.,[[[.,.],.],.]],[.,.]]] => 2
[[[]],[[[]],[],[]],[]] => [[.,.],[[[.,[.,[.,.]]],.],[.,.]]] => 2
[[[]],[[[]],[[]]],[]] => [[.,.],[[[.,[[.,.],.]],.],[.,.]]] => 2
[[[]],[[[],[]],[]],[]] => [[.,.],[[[.,[.,.]],[.,.]],[.,.]]] => 2
[[[]],[[[[]]],[]],[]] => [[.,.],[[[[.,[.,.]],.],.],[.,.]]] => 2
[[[]],[[[],[],[]]],[]] => [[.,.],[[[.,[.,[.,.]]],[.,.]],.]] => 2
[[[]],[[[],[[]]]],[]] => [[.,.],[[[.,[[.,.],.]],[.,.]],.]] => 2
[[[]],[[[[]],[]]],[]] => [[.,.],[[[[.,[.,.]],.],[.,.]],.]] => 2
[[[]],[[[[],[]]]],[]] => [[.,.],[[[[.,[.,.]],[.,.]],.],.]] => 2
[[[]],[[],[],[],[],[]]] => [[.,.],[[.,.],[.,[.,[.,[.,.]]]]]] => 2
[[[]],[[],[],[],[[]]]] => [[.,.],[[.,.],[.,[.,[[.,.],.]]]]] => 2
[[[]],[[],[],[[]],[]]] => [[.,.],[[.,.],[.,[[.,[.,.]],.]]]] => 2
[[[]],[[],[],[[],[]]]] => [[.,.],[[.,[.,[[.,.],[.,.]]]],.]] => 2
[[[]],[[],[],[[[]]]]] => [[.,.],[[.,.],[.,[[[.,.],.],.]]]] => 2
[[[]],[[],[[]],[],[]]] => [[.,.],[[.,.],[[.,[.,[.,.]]],.]]] => 2
[[[]],[[],[[]],[[]]]] => [[.,.],[[.,.],[[.,[[.,.],.]],.]]] => 2
[[[]],[[],[[],[]],[]]] => [[.,.],[[.,[[.,.],[.,.]]],[.,.]]] => 2
[[[]],[[],[[[]]],[]]] => [[.,.],[[.,.],[[[.,[.,.]],.],.]]] => 2
[[[]],[[],[[],[],[]]]] => [[.,.],[[.,[[.,.],[.,[.,.]]]],.]] => 2
[[[]],[[],[[],[[]]]]] => [[.,.],[[.,[[.,.],[[.,.],.]]],.]] => 2
[[[]],[[],[[[]],[]]]] => [[.,.],[[.,[[[.,.],.],[.,.]]],.]] => 2
[[[]],[[],[[[],[]]]]] => [[.,.],[[.,[[[.,.],[.,.]],.]],.]] => 2
[[[]],[[],[[[[]]]]]] => [[.,.],[[.,.],[[[[.,.],.],.],.]]] => 2
[[[]],[[[]],[],[],[]]] => [[.,.],[[[.,.],.],[.,[.,[.,.]]]]] => 2
[[[]],[[[]],[],[[]]]] => [[.,.],[[[.,.],.],[.,[[.,.],.]]]] => 2
[[[]],[[[]],[[]],[]]] => [[.,.],[[[.,.],.],[[.,[.,.]],.]]] => 2
[[[]],[[[]],[[],[]]]] => [[.,.],[[[.,.],[[.,.],[.,.]]],.]] => 2
[[[]],[[[]],[[[]]]]] => [[.,.],[[[.,.],.],[[[.,.],.],.]]] => 2
[[[]],[[[],[]],[],[]]] => [[.,.],[[[.,.],[.,.]],[.,[.,.]]]] => 2
[[[]],[[[[]]],[],[]]] => [[.,.],[[[[.,.],.],.],[.,[.,.]]]] => 2
[[[]],[[[],[]],[[]]]] => [[.,.],[[[.,.],[.,.]],[[.,.],.]]] => 2
[[[]],[[[[]]],[[]]]] => [[.,.],[[[[.,.],.],.],[[.,.],.]]] => 2
[[[]],[[[],[],[]],[]]] => [[.,.],[[[.,.],[.,[.,.]]],[.,.]]] => 2
[[[]],[[[],[[]]],[]]] => [[.,.],[[[.,.],[[.,.],.]],[.,.]]] => 2
[[[]],[[[[]],[]],[]]] => [[.,.],[[[[.,.],.],[.,.]],[.,.]]] => 2
[[[]],[[[[],[]]],[]]] => [[.,.],[[[[.,.],[.,.]],.],[.,.]]] => 2
[[[]],[[[[[]]]],[]]] => [[.,.],[[[[[.,.],.],.],.],[.,.]]] => 2
[[[]],[[[],[],[],[]]]] => [[.,.],[[[.,.],[.,[.,[.,.]]]],.]] => 2
[[[]],[[[],[],[[]]]]] => [[.,.],[[[.,.],[.,[[.,.],.]]],.]] => 2
[[[]],[[[],[[]],[]]]] => [[.,.],[[[.,.],[[.,[.,.]],.]],.]] => 2
[[[]],[[[],[[],[]]]]] => [[.,.],[[[.,[[.,.],[.,.]]],.],.]] => 2
[[[]],[[[],[[[]]]]]] => [[.,.],[[[.,.],[[[.,.],.],.]],.]] => 2
[[[]],[[[[]],[],[]]]] => [[.,.],[[[[.,.],.],[.,[.,.]]],.]] => 2
[[[]],[[[[]],[[]]]]] => [[.,.],[[[[.,.],.],[[.,.],.]],.]] => 2
[[[]],[[[[],[]],[]]]] => [[.,.],[[[[.,.],[.,.]],[.,.]],.]] => 2
[[[]],[[[[[]]],[]]]] => [[.,.],[[[[[.,.],.],.],[.,.]],.]] => 2
[[[]],[[[[],[],[]]]]] => [[.,.],[[[[.,.],[.,[.,.]]],.],.]] => 2
[[[]],[[[[],[[]]]]]] => [[.,.],[[[[.,.],[[.,.],.]],.],.]] => 2
[[[]],[[[[[]],[]]]]] => [[.,.],[[[[[.,.],.],[.,.]],.],.]] => 2
[[[]],[[[[[],[]]]]]] => [[.,.],[[[[[.,.],[.,.]],.],.],.]] => 2
[[[],[]],[],[],[],[],[]] => [[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]] => 2
[[[],[]],[],[],[],[[]]] => [[.,[.,.]],[.,[.,[.,[[.,.],.]]]]] => 2
[[[],[]],[],[],[[]],[]] => [[.,[.,.]],[.,[.,[[.,[.,.]],.]]]] => 2
[[[],[]],[],[],[[],[]]] => [[.,[.,.]],[.,[.,[[.,.],[.,.]]]]] => 2
[[[],[]],[],[],[[[]]]] => [[.,[.,.]],[.,[.,[[[.,.],.],.]]]] => 2
[[[],[]],[],[[]],[],[]] => [[.,[.,.]],[.,[[.,[.,[.,.]]],.]]] => 2
[[[],[]],[],[[]],[[]]] => [[.,[.,.]],[.,[[.,[[.,.],.]],.]]] => 2
[[[],[]],[],[[],[]],[]] => [[.,[.,.]],[.,[[.,[.,.]],[.,.]]]] => 2
[[[],[]],[],[[[]]],[]] => [[.,[.,.]],[.,[[[.,[.,.]],.],.]]] => 2
[[[],[]],[],[[],[],[]]] => [[.,[.,.]],[.,[[.,.],[.,[.,.]]]]] => 2
[[[],[]],[],[[],[[]]]] => [[.,[.,.]],[.,[[.,.],[[.,.],.]]]] => 2
[[[],[]],[],[[[]],[]]] => [[.,[.,.]],[.,[[[.,.],.],[.,.]]]] => 2
[[[],[]],[],[[[],[]]]] => [[.,[.,.]],[.,[[[.,.],[.,.]],.]]] => 2
[[[],[]],[],[[[[]]]]] => [[.,[.,.]],[.,[[[[.,.],.],.],.]]] => 2
[[[],[],[],[],[],[],[]]] => [[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]] => 2
[[[],[],[],[],[],[[]]]] => [[.,.],[.,[.,[.,[.,[[.,.],.]]]]]] => 2
[[[],[],[],[],[[]],[]]] => [[.,.],[.,[.,[.,[[.,[.,.]],.]]]]] => 2
[[[],[],[],[],[[[]]]]] => [[.,.],[.,[.,[.,[[[.,.],.],.]]]]] => 2
[[[],[],[],[[]],[],[]]] => [[.,.],[.,[.,[[.,[.,[.,.]]],.]]]] => 2
[[[],[],[],[[]],[[]]]] => [[.,.],[.,[.,[[.,[[.,.],.]],.]]]] => 2
[[[],[],[],[[[]]],[]]] => [[.,.],[.,[.,[[[.,[.,.]],.],.]]]] => 2
[[[],[],[],[[[[]]]]]] => [[.,.],[.,[.,[[[[.,.],.],.],.]]]] => 2
[[[],[],[[]],[],[],[]]] => [[.,.],[.,[[.,[.,[.,[.,.]]]],.]]] => 2
[[[],[],[[]],[],[[]]]] => [[.,.],[.,[[.,[.,[[.,.],.]]],.]]] => 2
[[[],[],[[]],[[]],[]]] => [[.,.],[.,[[.,[[.,[.,.]],.]],.]]] => 2
[[[],[],[[]],[[[]]]]] => [[.,.],[.,[[.,[[[.,.],.],.]],.]]] => 2
[[[],[],[[[]]],[],[]]] => [[.,.],[.,[[[.,[.,[.,.]]],.],.]]] => 2
[[[],[],[[[]]],[[]]]] => [[.,.],[.,[[[.,[[.,.],.]],.],.]]] => 2
[[[],[],[[[[]]]],[]]] => [[.,.],[.,[[[[.,[.,.]],.],.],.]]] => 2
[[[],[],[[[[[]]]]]]] => [[.,.],[.,[[[[[.,.],.],.],.],.]]] => 2
[[[],[[]],[],[],[],[]]] => [[.,.],[[.,[.,[.,[.,[.,.]]]]],.]] => 2
[[[],[[]],[],[],[[]]]] => [[.,.],[[.,[.,[.,[[.,.],.]]]],.]] => 2
[[[],[[]],[],[[]],[]]] => [[.,.],[[.,[.,[[.,[.,.]],.]]],.]] => 2
[[[],[[]],[],[[[]]]]] => [[.,.],[[.,[.,[[[.,.],.],.]]],.]] => 2
[[[],[[]],[[]],[],[]]] => [[.,.],[[.,[[.,[.,[.,.]]],.]],.]] => 2
[[[],[[]],[[]],[[]]]] => [[.,.],[[.,[[.,[[.,.],.]],.]],.]] => 2
[[[],[[]],[[[]]],[]]] => [[.,.],[[.,[[[.,[.,.]],.],.]],.]] => 2
[[[],[[]],[[[[]]]]]] => [[.,.],[[.,[[[[.,.],.],.],.]],.]] => 2
[[[],[[[]]],[],[],[]]] => [[.,.],[[[.,[.,[.,[.,.]]]],.],.]] => 2
[[[],[[[]]],[],[[]]]] => [[.,.],[[[.,[.,[[.,.],.]]],.],.]] => 2
[[[],[[[]]],[[]],[]]] => [[.,.],[[[.,[[.,[.,.]],.]],.],.]] => 2
[[[],[[[]]],[[[]]]]] => [[.,.],[[[.,[[[.,.],.],.]],.],.]] => 2
[[[],[[[[]]]],[],[]]] => [[.,.],[[[[.,[.,[.,.]]],.],.],.]] => 2
[[[],[[[[]]]],[[]]]] => [[.,.],[[[[.,[[.,.],.]],.],.],.]] => 2
[[[],[[[[[]]]]],[]]] => [[.,.],[[[[[.,[.,.]],.],.],.],.]] => 2
[[[],[[[[[[]]]]]]]] => [[.,.],[[[[[[.,.],.],.],.],.],.]] => 2
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 8,6 16,26 32,100 64,364,1
$F_{2} = q$
$F_{3} = 2\ q$
$F_{4} = 4\ q + q^{2}$
$F_{5} = 8\ q + 6\ q^{2}$
$F_{6} = 16\ q + 26\ q^{2}$
$F_{7} = 32\ q + 100\ q^{2}$
$F_{8} = 64\ q + 364\ q^{2} + q^{3}$
Description
The register function (or Horton-Strahler number) of a binary tree.
This is different from the dimension of the associated poset for the tree $[[[.,.],[.,.]],[[.,.],[.,.]]]$: its register function is 3, whereas the dimension of the associated poset is 2.
This is different from the dimension of the associated poset for the tree $[[[.,.],[.,.]],[[.,.],[.,.]]]$: its register function is 3, whereas the dimension of the associated poset is 2.
Map
Zeilberger's Strahler bijection
Description
Zeilberger's Strahler bijection between ordered and binary trees.
This is a bijection sending the pruning number of the ordered tree to the Strahler number of the binary tree.
This is a bijection sending the pruning number of the ordered tree to the Strahler number of the binary tree.
searching the database
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