Identifier
Values
[[]] => [.,.] => [1,0] => 1
[[],[]] => [.,[.,.]] => [1,0,1,0] => 1
[[[]]] => [[.,.],.] => [1,1,0,0] => 2
[[],[],[]] => [.,[.,[.,.]]] => [1,0,1,0,1,0] => 1
[[],[[]]] => [.,[[.,.],.]] => [1,0,1,1,0,0] => 1
[[[]],[]] => [[.,[.,.]],.] => [1,1,0,1,0,0] => 2
[[[],[]]] => [[.,.],[.,.]] => [1,1,0,0,1,0] => 1
[[[[]]]] => [[[.,.],.],.] => [1,1,1,0,0,0] => 3
[[],[],[],[]] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 1
[[],[],[[]]] => [.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => 1
[[],[[]],[]] => [.,[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0] => 1
[[],[[],[]]] => [.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => 1
[[],[[[]]]] => [.,[[[.,.],.],.]] => [1,0,1,1,1,0,0,0] => 1
[[[]],[],[]] => [[.,[.,[.,.]]],.] => [1,1,0,1,0,1,0,0] => 2
[[[]],[[]]] => [[.,[[.,.],.]],.] => [1,1,0,1,1,0,0,0] => 2
[[[],[]],[]] => [[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => 1
[[[[]]],[]] => [[[.,[.,.]],.],.] => [1,1,1,0,1,0,0,0] => 3
[[[],[],[]]] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => 1
[[[],[[]]]] => [[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => 2
[[[[]],[]]] => [[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0] => 1
[[[[],[]]]] => [[[.,.],[.,.]],.] => [1,1,1,0,0,1,0,0] => 2
[[[[[]]]]] => [[[[.,.],.],.],.] => [1,1,1,1,0,0,0,0] => 4
[[],[],[],[],[]] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 1
[[],[],[],[[]]] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => 1
[[],[],[[]],[]] => [.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,0,0] => 1
[[],[],[[],[]]] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => 1
[[],[],[[[]]]] => [.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,0,0] => 1
[[],[[]],[],[]] => [.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,0,0] => 1
[[],[[]],[[]]] => [.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,0,0] => 1
[[],[[],[]],[]] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => 1
[[],[[[]]],[]] => [.,[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,1,0,0,0] => 1
[[],[[],[],[]]] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => 1
[[],[[],[[]]]] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => 1
[[],[[[]],[]]] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0] => 1
[[],[[[],[]]]] => [.,[[[.,.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => 1
[[],[[[[]]]]] => [.,[[[[.,.],.],.],.]] => [1,0,1,1,1,1,0,0,0,0] => 1
[[[]],[],[],[]] => [[.,[.,[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,0,0] => 2
[[[]],[],[[]]] => [[.,[.,[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,0,0] => 2
[[[]],[[]],[]] => [[.,[[.,[.,.]],.]],.] => [1,1,0,1,1,0,1,0,0,0] => 2
[[[]],[[],[]]] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 1
[[[]],[[[]]]] => [[.,[[[.,.],.],.]],.] => [1,1,0,1,1,1,0,0,0,0] => 2
[[[],[]],[],[]] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 1
[[[[]]],[],[]] => [[[.,[.,[.,.]]],.],.] => [1,1,1,0,1,0,1,0,0,0] => 3
[[[],[]],[[]]] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 2
[[[[]]],[[]]] => [[[.,[[.,.],.]],.],.] => [1,1,1,0,1,1,0,0,0,0] => 3
[[[],[],[]],[]] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 1
[[[],[[]]],[]] => [[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => 1
[[[[]],[]],[]] => [[[.,[.,.]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0] => 1
[[[[],[]]],[]] => [[[.,[.,.]],[.,.]],.] => [1,1,1,0,1,0,0,1,0,0] => 2
[[[[[]]]],[]] => [[[[.,[.,.]],.],.],.] => [1,1,1,1,0,1,0,0,0,0] => 4
[[[],[],[],[]]] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 1
[[[],[],[[]]]] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => 1
[[[],[[]],[]]] => [[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => 2
[[[],[[],[]]]] => [[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,1,0,0] => 2
[[[],[[[]]]]] => [[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => 2
[[[[]],[],[]]] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => 1
[[[[]],[[]]]] => [[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => 2
[[[[],[]],[]]] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 1
[[[[[]]],[]]] => [[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0] => 1
[[[[],[],[]]]] => [[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => 2
[[[[],[[]]]]] => [[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => 3
[[[[[]],[]]]] => [[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => 2
[[[[[],[]]]]] => [[[[.,.],[.,.]],.],.] => [1,1,1,1,0,0,1,0,0,0] => 3
[[[[[[]]]]]] => [[[[[.,.],.],.],.],.] => [1,1,1,1,1,0,0,0,0,0] => 5
[[],[],[],[],[],[]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
[[],[],[],[],[[]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 1
[[],[],[],[[]],[]] => [.,[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 1
[[],[],[],[[],[]]] => [.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => 1
[[],[],[],[[[]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[[],[],[[]],[],[]] => [.,[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => 1
[[],[],[[]],[[]]] => [.,[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 1
[[],[],[[],[]],[]] => [.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 1
[[],[],[[[]]],[]] => [.,[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => 1
[[],[],[[],[],[]]] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 1
[[],[],[[],[[]]]] => [.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 1
[[],[],[[[]],[]]] => [.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[[],[],[[[],[]]]] => [.,[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 1
[[],[],[[[[]]]]] => [.,[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 1
[[],[[]],[],[],[]] => [.,[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => 1
[[],[[]],[],[[]]] => [.,[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,0] => 1
[[],[[]],[[]],[]] => [.,[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,0] => 1
[[],[[]],[[],[]]] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 1
[[],[[]],[[[]]]] => [.,[[.,[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,1,0,0,0,0] => 1
[[],[[],[]],[],[]] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 1
[[],[[[]]],[],[]] => [.,[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,0] => 1
[[],[[],[]],[[]]] => [.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 1
[[],[[[]]],[[]]] => [.,[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,0] => 1
[[],[[],[],[]],[]] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 1
[[],[[],[[]]],[]] => [.,[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,0] => 1
[[],[[[]],[]],[]] => [.,[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,0] => 1
[[],[[[],[]]],[]] => [.,[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => 1
[[],[[[[]]]],[]] => [.,[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,0] => 1
[[],[[],[],[],[]]] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 1
[[],[[],[],[[]]]] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 1
[[],[[],[[]],[]]] => [.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 1
[[],[[],[[],[]]]] => [.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => 1
[[],[[],[[[]]]]] => [.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[[],[[[]],[],[]]] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[[],[[[]],[[]]]] => [.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[[],[[[],[]],[]]] => [.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 1
[[],[[[[]]],[]]] => [.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0] => 1
>>> Load all 196 entries. <<<
[[],[[[],[],[]]]] => [.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 1
[[],[[[],[[]]]]] => [.,[[[.,.],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 1
[[],[[[[]],[]]]] => [.,[[[[.,.],.],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 1
[[],[[[[],[]]]]] => [.,[[[[.,.],[.,.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,0] => 1
[[],[[[[[]]]]]] => [.,[[[[[.,.],.],.],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 1
[[[]],[],[],[],[]] => [[.,[.,[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,0] => 2
[[[]],[],[],[[]]] => [[.,[.,[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0] => 2
[[[]],[],[[]],[]] => [[.,[.,[[.,[.,.]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0] => 2
[[[]],[],[[],[]]] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 1
[[[]],[],[[[]]]] => [[.,[.,[[[.,.],.],.]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0] => 2
[[[]],[[]],[],[]] => [[.,[[.,[.,[.,.]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,0,0] => 2
[[[]],[[]],[[]]] => [[.,[[.,[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,1,0,0,0,0] => 2
[[[]],[[],[]],[]] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 1
[[[]],[[[]]],[]] => [[.,[[[.,[.,.]],.],.]],.] => [1,1,0,1,1,1,0,1,0,0,0,0] => 2
[[[]],[[],[],[]]] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 1
[[[]],[[],[[]]]] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
[[[]],[[[]],[]]] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[[[]],[[[],[]]]] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 2
[[[]],[[[[]]]]] => [[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,0] => 2
[[[],[]],[],[],[]] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 1
[[[[]]],[],[],[]] => [[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,0,0] => 3
[[[],[]],[],[[]]] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 1
[[[[]]],[],[[]]] => [[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,1,1,0,0,0,0] => 3
[[[],[]],[[]],[]] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 2
[[[[]]],[[]],[]] => [[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,1,1,0,1,0,0,0,0] => 3
[[[],[]],[[],[]]] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 1
[[[],[]],[[[]]]] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 2
[[[[]]],[[],[]]] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[[[[]]],[[[]]]] => [[[.,[[[.,.],.],.]],.],.] => [1,1,1,0,1,1,1,0,0,0,0,0] => 3
[[[],[],[]],[],[]] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 1
[[[],[[]]],[],[]] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 1
[[[[]],[]],[],[]] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 1
[[[[],[]]],[],[]] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => 2
[[[[[]]]],[],[]] => [[[[.,[.,[.,.]]],.],.],.] => [1,1,1,1,0,1,0,1,0,0,0,0] => 4
[[[],[],[]],[[]]] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 2
[[[],[[]]],[[]]] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 2
[[[[]],[]],[[]]] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 2
[[[[],[]]],[[]]] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => 3
[[[[[]]]],[[]]] => [[[[.,[[.,.],.]],.],.],.] => [1,1,1,1,0,1,1,0,0,0,0,0] => 4
[[[],[],[],[]],[]] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 1
[[[],[],[[]]],[]] => [[.,[.,[[.,.],.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0] => 1
[[[],[[]],[]],[]] => [[.,[[.,[.,.]],.]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,0] => 1
[[[],[[],[]]],[]] => [[.,[[.,[.,.]],[.,.]]],.] => [1,1,0,1,1,0,1,0,0,1,0,0] => 2
[[[],[[[]]]],[]] => [[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0] => 1
[[[[]],[],[]],[]] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,0] => 1
[[[[]],[[]]],[]] => [[[.,[[.,.],.]],.],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,0] => 1
[[[[],[]],[]],[]] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 1
[[[[[]]],[]],[]] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,0] => 1
[[[[],[],[]]],[]] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0] => 2
[[[[],[[]]]],[]] => [[[.,[[.,.],.]],[.,.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0] => 2
[[[[[]],[]]],[]] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0] => 2
[[[[[],[]]]],[]] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,1,1,0,1,0,0,1,0,0,0] => 3
[[[[[[]]]]],[]] => [[[[[.,[.,.]],.],.],.],.] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[[[],[],[],[],[]]] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 1
[[[],[],[],[[]]]] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 1
[[[],[],[[]],[]]] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 1
[[[],[],[[],[]]]] => [[.,[.,[[.,.],[.,.]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,0] => 2
[[[],[],[[[]]]]] => [[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[[[],[[]],[],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 2
[[[],[[]],[[]]]] => [[.,.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 2
[[[],[[],[]],[]]] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 1
[[[],[[[]]],[]]] => [[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 2
[[[],[[],[],[]]]] => [[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => 2
[[[],[[],[[]]]]] => [[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0] => 2
[[[],[[[]],[]]]] => [[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,1,1,0,0,0,1,0,0] => 2
[[[],[[[],[]]]]] => [[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,1,0,0,1,0,0,0] => 2
[[[],[[[[]]]]]] => [[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[[[[]],[],[],[]]] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[[[[]],[],[[]]]] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[[[[]],[[]],[]]] => [[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 2
[[[[]],[[],[]]]] => [[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => 2
[[[[]],[[[]]]]] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[[[[],[]],[],[]]] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 1
[[[[[]]],[],[]]] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 1
[[[[],[]],[[]]]] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 2
[[[[[]]],[[]]]] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[[[[],[],[]],[]]] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 1
[[[[],[[]]],[]]] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 1
[[[[[]],[]],[]]] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 1
[[[[[],[]]],[]]] => [[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 1
[[[[[[]]]],[]]] => [[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => 1
[[[[],[],[],[]]]] => [[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => 2
[[[[],[],[[]]]]] => [[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => 2
[[[[],[[]],[]]]] => [[[.,.],[[.,[.,.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,0] => 3
[[[[],[[],[]]]]] => [[[.,[[.,.],[.,.]]],.],.] => [1,1,1,0,1,1,0,0,1,0,0,0] => 3
[[[[],[[[]]]]]] => [[[.,.],[[[.,.],.],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,0] => 3
[[[[[]],[],[]]]] => [[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => 2
[[[[[]],[[]]]]] => [[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => 3
[[[[[],[]],[]]]] => [[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => 2
[[[[[[]]],[]]]] => [[[[[.,.],.],.],[.,.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0] => 2
[[[[[],[],[]]]]] => [[[[.,.],[.,[.,.]]],.],.] => [1,1,1,1,0,0,1,0,1,0,0,0] => 3
[[[[[],[[]]]]]] => [[[[.,.],[[.,.],.]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0] => 4
[[[[[[]],[]]]]] => [[[[[.,.],.],[.,.]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0] => 3
[[[[[[],[]]]]]] => [[[[[.,.],[.,.]],.],.],.] => [1,1,1,1,1,0,0,1,0,0,0,0] => 4
[[[[[[[]]]]]]] => [[[[[[.,.],.],.],.],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
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Description
The minimal height of a peak of a Dyck path.
Map
to Dyck path: up step, left tree, down step, right tree
Description
Return the associated Dyck path, using the bijection 1L0R.
This is given recursively as follows:
  • a leaf is associated to the empty Dyck Word
  • a tree with children $l,r$ is associated with the Dyck path described by 1L0R where $L$ and $R$ are respectively the Dyck words associated with the trees $l$ and $r$.
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.