Identifier
Values
[[]] => [[]] => 1
[[],[]] => [[[]]] => 1
[[[]]] => [[],[]] => 2
[[],[],[]] => [[[[]]]] => 1
[[],[[]]] => [[[],[]]] => 2
[[[]],[]] => [[],[[]]] => 2
[[[],[]]] => [[[]],[]] => 2
[[[[]]]] => [[],[],[]] => 3
[[],[],[],[]] => [[[[[]]]]] => 1
[[],[],[[]]] => [[[[],[]]]] => 2
[[],[[]],[]] => [[[],[[]]]] => 2
[[],[[],[]]] => [[[[]],[]]] => 2
[[],[[[]]]] => [[[],[],[]]] => 3
[[[]],[],[]] => [[],[[[]]]] => 2
[[[]],[[]]] => [[],[[],[]]] => 3
[[[],[]],[]] => [[[]],[[]]] => 2
[[[[]]],[]] => [[],[],[[]]] => 3
[[[],[],[]]] => [[[[]]],[]] => 2
[[[],[[]]]] => [[[],[]],[]] => 3
[[[[]],[]]] => [[],[[]],[]] => 3
[[[[],[]]]] => [[[]],[],[]] => 3
[[[[[]]]]] => [[],[],[],[]] => 4
[[],[],[],[],[]] => [[[[[[]]]]]] => 1
[[],[],[],[[]]] => [[[[[],[]]]]] => 2
[[],[],[[]],[]] => [[[[],[[]]]]] => 2
[[],[],[[],[]]] => [[[[[]],[]]]] => 2
[[],[],[[[]]]] => [[[[],[],[]]]] => 3
[[],[[]],[],[]] => [[[],[[[]]]]] => 2
[[],[[]],[[]]] => [[[],[[],[]]]] => 3
[[],[[],[]],[]] => [[[[]],[[]]]] => 2
[[],[[[]]],[]] => [[[],[],[[]]]] => 3
[[],[[],[],[]]] => [[[[[]]],[]]] => 2
[[],[[],[[]]]] => [[[[],[]],[]]] => 3
[[],[[[]],[]]] => [[[],[[]],[]]] => 3
[[],[[[],[]]]] => [[[[]],[],[]]] => 3
[[],[[[[]]]]] => [[[],[],[],[]]] => 4
[[[]],[],[],[]] => [[],[[[[]]]]] => 2
[[[]],[],[[]]] => [[],[[[],[]]]] => 3
[[[]],[[]],[]] => [[],[[],[[]]]] => 3
[[[]],[[],[]]] => [[],[[[]],[]]] => 3
[[[]],[[[]]]] => [[],[[],[],[]]] => 4
[[[],[]],[],[]] => [[[]],[[[]]]] => 2
[[[[]]],[],[]] => [[],[],[[[]]]] => 3
[[[],[]],[[]]] => [[[]],[[],[]]] => 3
[[[[]]],[[]]] => [[],[],[[],[]]] => 4
[[[],[],[]],[]] => [[[[]]],[[]]] => 2
[[[],[[]]],[]] => [[[],[]],[[]]] => 3
[[[[]],[]],[]] => [[],[[]],[[]]] => 3
[[[[],[]]],[]] => [[[]],[],[[]]] => 3
[[[[[]]]],[]] => [[],[],[],[[]]] => 4
[[[],[],[],[]]] => [[[[[]]]],[]] => 2
[[[],[],[[]]]] => [[[[],[]]],[]] => 3
[[[],[[]],[]]] => [[[],[[]]],[]] => 3
[[[],[[],[]]]] => [[[[]],[]],[]] => 3
[[[],[[[]]]]] => [[[],[],[]],[]] => 4
[[[[]],[],[]]] => [[],[[[]]],[]] => 3
[[[[]],[[]]]] => [[],[[],[]],[]] => 4
[[[[],[]],[]]] => [[[]],[[]],[]] => 3
[[[[[]]],[]]] => [[],[],[[]],[]] => 4
[[[[],[],[]]]] => [[[[]]],[],[]] => 3
[[[[],[[]]]]] => [[[],[]],[],[]] => 4
[[[[[]],[]]]] => [[],[[]],[],[]] => 4
[[[[[],[]]]]] => [[[]],[],[],[]] => 4
[[[[[[]]]]]] => [[],[],[],[],[]] => 5
[[],[],[],[],[],[]] => [[[[[[[]]]]]]] => 1
[[],[],[],[],[[]]] => [[[[[[],[]]]]]] => 2
[[],[],[],[[]],[]] => [[[[[],[[]]]]]] => 2
[[],[],[],[[],[]]] => [[[[[[]],[]]]]] => 2
[[],[],[],[[[]]]] => [[[[[],[],[]]]]] => 3
[[],[],[[]],[],[]] => [[[[],[[[]]]]]] => 2
[[],[],[[]],[[]]] => [[[[],[[],[]]]]] => 3
[[],[],[[],[]],[]] => [[[[[]],[[]]]]] => 2
[[],[],[[[]]],[]] => [[[[],[],[[]]]]] => 3
[[],[],[[],[],[]]] => [[[[[[]]],[]]]] => 2
[[],[],[[],[[]]]] => [[[[[],[]],[]]]] => 3
[[],[],[[[]],[]]] => [[[[],[[]],[]]]] => 3
[[],[],[[[],[]]]] => [[[[[]],[],[]]]] => 3
[[],[],[[[[]]]]] => [[[[],[],[],[]]]] => 4
[[],[[]],[],[],[]] => [[[],[[[[]]]]]] => 2
[[],[[]],[],[[]]] => [[[],[[[],[]]]]] => 3
[[],[[]],[[]],[]] => [[[],[[],[[]]]]] => 3
[[],[[]],[[],[]]] => [[[],[[[]],[]]]] => 3
[[],[[]],[[[]]]] => [[[],[[],[],[]]]] => 4
[[],[[],[]],[],[]] => [[[[]],[[[]]]]] => 2
[[],[[[]]],[],[]] => [[[],[],[[[]]]]] => 3
[[],[[],[]],[[]]] => [[[[]],[[],[]]]] => 3
[[],[[[]]],[[]]] => [[[],[],[[],[]]]] => 4
[[],[[],[],[]],[]] => [[[[[]]],[[]]]] => 2
[[],[[],[[]]],[]] => [[[[],[]],[[]]]] => 3
[[],[[[]],[]],[]] => [[[],[[]],[[]]]] => 3
[[],[[[],[]]],[]] => [[[[]],[],[[]]]] => 3
[[],[[[[]]]],[]] => [[[],[],[],[[]]]] => 4
[[],[[],[],[],[]]] => [[[[[[]]]],[]]] => 2
[[],[[],[],[[]]]] => [[[[[],[]]],[]]] => 3
[[],[[],[[]],[]]] => [[[[],[[]]],[]]] => 3
[[],[[],[[],[]]]] => [[[[[]],[]],[]]] => 3
[[],[[],[[[]]]]] => [[[[],[],[]],[]]] => 4
[[],[[[]],[],[]]] => [[[],[[[]]],[]]] => 3
[[],[[[]],[[]]]] => [[[],[[],[]],[]]] => 4
[[],[[[],[]],[]]] => [[[[]],[[]],[]]] => 3
[[],[[[[]]],[]]] => [[[],[],[[]],[]]] => 4
>>> Load all 483 entries. <<<
[[],[[[],[],[]]]] => [[[[[]]],[],[]]] => 3
[[],[[[],[[]]]]] => [[[[],[]],[],[]]] => 4
[[],[[[[]],[]]]] => [[[],[[]],[],[]]] => 4
[[],[[[[],[]]]]] => [[[[]],[],[],[]]] => 4
[[],[[[[[]]]]]] => [[[],[],[],[],[]]] => 5
[[[]],[],[],[],[]] => [[],[[[[[]]]]]] => 2
[[[]],[],[],[[]]] => [[],[[[[],[]]]]] => 3
[[[]],[],[[]],[]] => [[],[[[],[[]]]]] => 3
[[[]],[],[[],[]]] => [[],[[[[]],[]]]] => 3
[[[]],[],[[[]]]] => [[],[[[],[],[]]]] => 4
[[[]],[[]],[],[]] => [[],[[],[[[]]]]] => 3
[[[]],[[]],[[]]] => [[],[[],[[],[]]]] => 4
[[[]],[[],[]],[]] => [[],[[[]],[[]]]] => 3
[[[]],[[[]]],[]] => [[],[[],[],[[]]]] => 4
[[[]],[[],[],[]]] => [[],[[[[]]],[]]] => 3
[[[]],[[],[[]]]] => [[],[[[],[]],[]]] => 4
[[[]],[[[]],[]]] => [[],[[],[[]],[]]] => 4
[[[]],[[[],[]]]] => [[],[[[]],[],[]]] => 4
[[[]],[[[[]]]]] => [[],[[],[],[],[]]] => 5
[[[],[]],[],[],[]] => [[[]],[[[[]]]]] => 2
[[[[]]],[],[],[]] => [[],[],[[[[]]]]] => 3
[[[],[]],[],[[]]] => [[[]],[[[],[]]]] => 3
[[[[]]],[],[[]]] => [[],[],[[[],[]]]] => 4
[[[],[]],[[]],[]] => [[[]],[[],[[]]]] => 3
[[[[]]],[[]],[]] => [[],[],[[],[[]]]] => 4
[[[],[]],[[],[]]] => [[[]],[[[]],[]]] => 3
[[[],[]],[[[]]]] => [[[]],[[],[],[]]] => 4
[[[[]]],[[],[]]] => [[],[],[[[]],[]]] => 4
[[[[]]],[[[]]]] => [[],[],[[],[],[]]] => 5
[[[],[],[]],[],[]] => [[[[]]],[[[]]]] => 2
[[[],[[]]],[],[]] => [[[],[]],[[[]]]] => 3
[[[[]],[]],[],[]] => [[],[[]],[[[]]]] => 3
[[[[],[]]],[],[]] => [[[]],[],[[[]]]] => 3
[[[[[]]]],[],[]] => [[],[],[],[[[]]]] => 4
[[[],[],[]],[[]]] => [[[[]]],[[],[]]] => 3
[[[],[[]]],[[]]] => [[[],[]],[[],[]]] => 4
[[[[]],[]],[[]]] => [[],[[]],[[],[]]] => 4
[[[[],[]]],[[]]] => [[[]],[],[[],[]]] => 4
[[[[[]]]],[[]]] => [[],[],[],[[],[]]] => 5
[[[],[],[],[]],[]] => [[[[[]]]],[[]]] => 2
[[[],[],[[]]],[]] => [[[[],[]]],[[]]] => 3
[[[],[[]],[]],[]] => [[[],[[]]],[[]]] => 3
[[[],[[],[]]],[]] => [[[[]],[]],[[]]] => 3
[[[],[[[]]]],[]] => [[[],[],[]],[[]]] => 4
[[[[]],[],[]],[]] => [[],[[[]]],[[]]] => 3
[[[[]],[[]]],[]] => [[],[[],[]],[[]]] => 4
[[[[],[]],[]],[]] => [[[]],[[]],[[]]] => 3
[[[[[]]],[]],[]] => [[],[],[[]],[[]]] => 4
[[[[],[],[]]],[]] => [[[[]]],[],[[]]] => 3
[[[[],[[]]]],[]] => [[[],[]],[],[[]]] => 4
[[[[[]],[]]],[]] => [[],[[]],[],[[]]] => 4
[[[[[],[]]]],[]] => [[[]],[],[],[[]]] => 4
[[[[[[]]]]],[]] => [[],[],[],[],[[]]] => 5
[[[],[],[],[],[]]] => [[[[[[]]]]],[]] => 2
[[[],[],[],[[]]]] => [[[[[],[]]]],[]] => 3
[[[],[],[[]],[]]] => [[[[],[[]]]],[]] => 3
[[[],[],[[],[]]]] => [[[[[]],[]]],[]] => 3
[[[],[],[[[]]]]] => [[[[],[],[]]],[]] => 4
[[[],[[]],[],[]]] => [[[],[[[]]]],[]] => 3
[[[],[[]],[[]]]] => [[[],[[],[]]],[]] => 4
[[[],[[],[]],[]]] => [[[[]],[[]]],[]] => 3
[[[],[[[]]],[]]] => [[[],[],[[]]],[]] => 4
[[[],[[],[],[]]]] => [[[[[]]],[]],[]] => 3
[[[],[[],[[]]]]] => [[[[],[]],[]],[]] => 4
[[[],[[[]],[]]]] => [[[],[[]],[]],[]] => 4
[[[],[[[],[]]]]] => [[[[]],[],[]],[]] => 4
[[[],[[[[]]]]]] => [[[],[],[],[]],[]] => 5
[[[[]],[],[],[]]] => [[],[[[[]]]],[]] => 3
[[[[]],[],[[]]]] => [[],[[[],[]]],[]] => 4
[[[[]],[[]],[]]] => [[],[[],[[]]],[]] => 4
[[[[]],[[],[]]]] => [[],[[[]],[]],[]] => 4
[[[[]],[[[]]]]] => [[],[[],[],[]],[]] => 5
[[[[],[]],[],[]]] => [[[]],[[[]]],[]] => 3
[[[[[]]],[],[]]] => [[],[],[[[]]],[]] => 4
[[[[],[]],[[]]]] => [[[]],[[],[]],[]] => 4
[[[[[]]],[[]]]] => [[],[],[[],[]],[]] => 5
[[[[],[],[]],[]]] => [[[[]]],[[]],[]] => 3
[[[[],[[]]],[]]] => [[[],[]],[[]],[]] => 4
[[[[[]],[]],[]]] => [[],[[]],[[]],[]] => 4
[[[[[],[]]],[]]] => [[[]],[],[[]],[]] => 4
[[[[[[]]]],[]]] => [[],[],[],[[]],[]] => 5
[[[[],[],[],[]]]] => [[[[[]]]],[],[]] => 3
[[[[],[],[[]]]]] => [[[[],[]]],[],[]] => 4
[[[[],[[]],[]]]] => [[[],[[]]],[],[]] => 4
[[[[],[[],[]]]]] => [[[[]],[]],[],[]] => 4
[[[[],[[[]]]]]] => [[[],[],[]],[],[]] => 5
[[[[[]],[],[]]]] => [[],[[[]]],[],[]] => 4
[[[[[]],[[]]]]] => [[],[[],[]],[],[]] => 5
[[[[[],[]],[]]]] => [[[]],[[]],[],[]] => 4
[[[[[[]]],[]]]] => [[],[],[[]],[],[]] => 5
[[[[[],[],[]]]]] => [[[[]]],[],[],[]] => 4
[[[[[],[[]]]]]] => [[[],[]],[],[],[]] => 5
[[[[[[]],[]]]]] => [[],[[]],[],[],[]] => 5
[[[[[[],[]]]]]] => [[[]],[],[],[],[]] => 5
[[[[[[[]]]]]]] => [[],[],[],[],[],[]] => 6
[[],[],[],[],[],[],[]] => [[[[[[[[]]]]]]]] => 1
[[],[],[],[],[],[[]]] => [[[[[[[],[]]]]]]] => 2
[[],[],[],[],[[]],[]] => [[[[[[],[[]]]]]]] => 2
[[],[],[],[],[[],[]]] => [[[[[[[]],[]]]]]] => 2
[[],[],[],[],[[[]]]] => [[[[[[],[],[]]]]]] => 3
[[],[],[],[[]],[],[]] => [[[[[],[[[]]]]]]] => 2
[[],[],[],[[]],[[]]] => [[[[[],[[],[]]]]]] => 3
[[],[],[],[[],[]],[]] => [[[[[[]],[[]]]]]] => 2
[[],[],[],[[[]]],[]] => [[[[[],[],[[]]]]]] => 3
[[],[],[],[[],[],[]]] => [[[[[[[]]],[]]]]] => 2
[[],[],[],[[],[[]]]] => [[[[[[],[]],[]]]]] => 3
[[],[],[],[[[]],[]]] => [[[[[],[[]],[]]]]] => 3
[[],[],[],[[[],[]]]] => [[[[[[]],[],[]]]]] => 3
[[],[],[],[[[[]]]]] => [[[[[],[],[],[]]]]] => 4
[[],[],[[]],[],[],[]] => [[[[],[[[[]]]]]]] => 2
[[],[],[[]],[],[[]]] => [[[[],[[[],[]]]]]] => 3
[[],[],[[]],[[]],[]] => [[[[],[[],[[]]]]]] => 3
[[],[],[[]],[[],[]]] => [[[[],[[[]],[]]]]] => 3
[[],[],[[]],[[[]]]] => [[[[],[[],[],[]]]]] => 4
[[],[],[[],[]],[],[]] => [[[[[]],[[[]]]]]] => 2
[[],[],[[[]]],[],[]] => [[[[],[],[[[]]]]]] => 3
[[],[],[[],[]],[[]]] => [[[[[]],[[],[]]]]] => 3
[[],[],[[[]]],[[]]] => [[[[],[],[[],[]]]]] => 4
[[],[],[[],[],[]],[]] => [[[[[[]]],[[]]]]] => 2
[[],[],[[],[[]]],[]] => [[[[[],[]],[[]]]]] => 3
[[],[],[[[]],[]],[]] => [[[[],[[]],[[]]]]] => 3
[[],[],[[[],[]]],[]] => [[[[[]],[],[[]]]]] => 3
[[],[],[[[[]]]],[]] => [[[[],[],[],[[]]]]] => 4
[[],[],[[],[],[],[]]] => [[[[[[[]]]],[]]]] => 2
[[],[],[[],[],[[]]]] => [[[[[[],[]]],[]]]] => 3
[[],[],[[],[[]],[]]] => [[[[[],[[]]],[]]]] => 3
[[],[],[[],[[],[]]]] => [[[[[[]],[]],[]]]] => 3
[[],[],[[],[[[]]]]] => [[[[[],[],[]],[]]]] => 4
[[],[],[[[]],[],[]]] => [[[[],[[[]]],[]]]] => 3
[[],[],[[[]],[[]]]] => [[[[],[[],[]],[]]]] => 4
[[],[],[[[],[]],[]]] => [[[[[]],[[]],[]]]] => 3
[[],[],[[[[]]],[]]] => [[[[],[],[[]],[]]]] => 4
[[],[],[[[],[],[]]]] => [[[[[[]]],[],[]]]] => 3
[[],[],[[[],[[]]]]] => [[[[[],[]],[],[]]]] => 4
[[],[],[[[[]],[]]]] => [[[[],[[]],[],[]]]] => 4
[[],[],[[[[],[]]]]] => [[[[[]],[],[],[]]]] => 4
[[],[],[[[[[]]]]]] => [[[[],[],[],[],[]]]] => 5
[[],[[]],[],[],[],[]] => [[[],[[[[[]]]]]]] => 2
[[],[[]],[],[],[[]]] => [[[],[[[[],[]]]]]] => 3
[[],[[]],[],[[]],[]] => [[[],[[[],[[]]]]]] => 3
[[],[[]],[],[[],[]]] => [[[],[[[[]],[]]]]] => 3
[[],[[]],[],[[[]]]] => [[[],[[[],[],[]]]]] => 4
[[],[[]],[[]],[],[]] => [[[],[[],[[[]]]]]] => 3
[[],[[]],[[]],[[]]] => [[[],[[],[[],[]]]]] => 4
[[],[[]],[[],[]],[]] => [[[],[[[]],[[]]]]] => 3
[[],[[]],[[[]]],[]] => [[[],[[],[],[[]]]]] => 4
[[],[[]],[[],[],[]]] => [[[],[[[[]]],[]]]] => 3
[[],[[]],[[],[[]]]] => [[[],[[[],[]],[]]]] => 4
[[],[[]],[[[]],[]]] => [[[],[[],[[]],[]]]] => 4
[[],[[]],[[[],[]]]] => [[[],[[[]],[],[]]]] => 4
[[],[[]],[[[[]]]]] => [[[],[[],[],[],[]]]] => 5
[[],[[],[]],[],[],[]] => [[[[]],[[[[]]]]]] => 2
[[],[[[]]],[],[],[]] => [[[],[],[[[[]]]]]] => 3
[[],[[],[]],[],[[]]] => [[[[]],[[[],[]]]]] => 3
[[],[[[]]],[],[[]]] => [[[],[],[[[],[]]]]] => 4
[[],[[],[]],[[]],[]] => [[[[]],[[],[[]]]]] => 3
[[],[[[]]],[[]],[]] => [[[],[],[[],[[]]]]] => 4
[[],[[],[]],[[],[]]] => [[[[]],[[[]],[]]]] => 3
[[],[[],[]],[[[]]]] => [[[[]],[[],[],[]]]] => 4
[[],[[[]]],[[],[]]] => [[[],[],[[[]],[]]]] => 4
[[],[[[]]],[[[]]]] => [[[],[],[[],[],[]]]] => 5
[[],[[],[],[]],[],[]] => [[[[[]]],[[[]]]]] => 2
[[],[[],[[]]],[],[]] => [[[[],[]],[[[]]]]] => 3
[[],[[[]],[]],[],[]] => [[[],[[]],[[[]]]]] => 3
[[],[[[],[]]],[],[]] => [[[[]],[],[[[]]]]] => 3
[[],[[[[]]]],[],[]] => [[[],[],[],[[[]]]]] => 4
[[],[[],[],[]],[[]]] => [[[[[]]],[[],[]]]] => 3
[[],[[],[[]]],[[]]] => [[[[],[]],[[],[]]]] => 4
[[],[[[]],[]],[[]]] => [[[],[[]],[[],[]]]] => 4
[[],[[[],[]]],[[]]] => [[[[]],[],[[],[]]]] => 4
[[],[[[[]]]],[[]]] => [[[],[],[],[[],[]]]] => 5
[[],[[],[],[],[]],[]] => [[[[[[]]]],[[]]]] => 2
[[],[[],[],[[]]],[]] => [[[[[],[]]],[[]]]] => 3
[[],[[],[[]],[]],[]] => [[[[],[[]]],[[]]]] => 3
[[],[[],[[],[]]],[]] => [[[[[]],[]],[[]]]] => 3
[[],[[],[[[]]]],[]] => [[[[],[],[]],[[]]]] => 4
[[],[[[]],[],[]],[]] => [[[],[[[]]],[[]]]] => 3
[[],[[[]],[[]]],[]] => [[[],[[],[]],[[]]]] => 4
[[],[[[],[]],[]],[]] => [[[[]],[[]],[[]]]] => 3
[[],[[[[]]],[]],[]] => [[[],[],[[]],[[]]]] => 4
[[],[[[],[],[]]],[]] => [[[[[]]],[],[[]]]] => 3
[[],[[[],[[]]]],[]] => [[[[],[]],[],[[]]]] => 4
[[],[[[[]],[]]],[]] => [[[],[[]],[],[[]]]] => 4
[[],[[[[],[]]]],[]] => [[[[]],[],[],[[]]]] => 4
[[],[[[[[]]]]],[]] => [[[],[],[],[],[[]]]] => 5
[[],[[],[],[],[],[]]] => [[[[[[[]]]]],[]]] => 2
[[],[[],[],[],[[]]]] => [[[[[[],[]]]],[]]] => 3
[[],[[],[],[[]],[]]] => [[[[[],[[]]]],[]]] => 3
[[],[[],[],[[],[]]]] => [[[[[[]],[]]],[]]] => 3
[[],[[],[],[[[]]]]] => [[[[[],[],[]]],[]]] => 4
[[],[[],[[]],[],[]]] => [[[[],[[[]]]],[]]] => 3
[[],[[],[[]],[[]]]] => [[[[],[[],[]]],[]]] => 4
[[],[[],[[],[]],[]]] => [[[[[]],[[]]],[]]] => 3
[[],[[],[[[]]],[]]] => [[[[],[],[[]]],[]]] => 4
[[],[[],[[],[],[]]]] => [[[[[[]]],[]],[]]] => 3
[[],[[],[[],[[]]]]] => [[[[[],[]],[]],[]]] => 4
[[],[[],[[[]],[]]]] => [[[[],[[]],[]],[]]] => 4
[[],[[],[[[],[]]]]] => [[[[[]],[],[]],[]]] => 4
[[],[[],[[[[]]]]]] => [[[[],[],[],[]],[]]] => 5
[[],[[[]],[],[],[]]] => [[[],[[[[]]]],[]]] => 3
[[],[[[]],[],[[]]]] => [[[],[[[],[]]],[]]] => 4
[[],[[[]],[[]],[]]] => [[[],[[],[[]]],[]]] => 4
[[],[[[]],[[],[]]]] => [[[],[[[]],[]],[]]] => 4
[[],[[[]],[[[]]]]] => [[[],[[],[],[]],[]]] => 5
[[],[[[],[]],[],[]]] => [[[[]],[[[]]],[]]] => 3
[[],[[[[]]],[],[]]] => [[[],[],[[[]]],[]]] => 4
[[],[[[],[]],[[]]]] => [[[[]],[[],[]],[]]] => 4
[[],[[[[]]],[[]]]] => [[[],[],[[],[]],[]]] => 5
[[],[[[],[],[]],[]]] => [[[[[]]],[[]],[]]] => 3
[[],[[[],[[]]],[]]] => [[[[],[]],[[]],[]]] => 4
[[],[[[[]],[]],[]]] => [[[],[[]],[[]],[]]] => 4
[[],[[[[],[]]],[]]] => [[[[]],[],[[]],[]]] => 4
[[],[[[[[]]]],[]]] => [[[],[],[],[[]],[]]] => 5
[[],[[[],[],[],[]]]] => [[[[[[]]]],[],[]]] => 3
[[],[[[],[],[[]]]]] => [[[[[],[]]],[],[]]] => 4
[[],[[[],[[]],[]]]] => [[[[],[[]]],[],[]]] => 4
[[],[[[],[[],[]]]]] => [[[[[]],[]],[],[]]] => 4
[[],[[[],[[[]]]]]] => [[[[],[],[]],[],[]]] => 5
[[],[[[[]],[],[]]]] => [[[],[[[]]],[],[]]] => 4
[[],[[[[]],[[]]]]] => [[[],[[],[]],[],[]]] => 5
[[],[[[[],[]],[]]]] => [[[[]],[[]],[],[]]] => 4
[[],[[[[[]]],[]]]] => [[[],[],[[]],[],[]]] => 5
[[],[[[[],[],[]]]]] => [[[[[]]],[],[],[]]] => 4
[[],[[[[],[[]]]]]] => [[[[],[]],[],[],[]]] => 5
[[],[[[[[]],[]]]]] => [[[],[[]],[],[],[]]] => 5
[[],[[[[[],[]]]]]] => [[[[]],[],[],[],[]]] => 5
[[],[[[[[[]]]]]]] => [[[],[],[],[],[],[]]] => 6
[[[]],[],[],[],[],[]] => [[],[[[[[[]]]]]]] => 2
[[[]],[],[],[],[[]]] => [[],[[[[[],[]]]]]] => 3
[[[]],[],[],[[]],[]] => [[],[[[[],[[]]]]]] => 3
[[[]],[],[],[[],[]]] => [[],[[[[[]],[]]]]] => 3
[[[]],[],[],[[[]]]] => [[],[[[[],[],[]]]]] => 4
[[[]],[],[[]],[],[]] => [[],[[[],[[[]]]]]] => 3
[[[]],[],[[]],[[]]] => [[],[[[],[[],[]]]]] => 4
[[[]],[],[[],[]],[]] => [[],[[[[]],[[]]]]] => 3
[[[]],[],[[],[],[]]] => [[],[[[[[]]],[]]]] => 3
[[[]],[],[[],[[]]]] => [[],[[[[],[]],[]]]] => 4
[[[]],[[]],[],[],[]] => [[],[[],[[[[]]]]]] => 3
[[[]],[[],[],[],[]]] => [[],[[[[[]]]],[]]] => 3
[[[]],[[],[],[[]]]] => [[],[[[[],[]]],[]]] => 4
[[[]],[[],[[]],[]]] => [[],[[[],[[]]],[]]] => 4
[[[]],[[],[[[]]]]] => [[],[[[],[],[]],[]]] => 5
[[[]],[[[],[],[]]]] => [[],[[[[]]],[],[]]] => 4
[[[]],[[[],[[]]]]] => [[],[[[],[]],[],[]]] => 5
[[[]],[[[[],[]]]]] => [[],[[[]],[],[],[]]] => 5
[[[]],[[[[[]]]]]] => [[],[[],[],[],[],[]]] => 6
[[[],[]],[],[],[],[]] => [[[]],[[[[[]]]]]] => 2
[[[[]]],[],[],[],[]] => [[],[],[[[[[]]]]]] => 3
[[[[]]],[],[],[[]]] => [[],[],[[[[],[]]]]] => 4
[[[[]]],[],[[]],[]] => [[],[],[[[],[[]]]]] => 4
[[[[]]],[],[[[]]]] => [[],[],[[[],[],[]]]] => 5
[[[[]]],[[],[],[]]] => [[],[],[[[[]]],[]]] => 4
[[[[]]],[[],[[]]]] => [[],[],[[[],[]],[]]] => 5
[[[[]]],[[[],[]]]] => [[],[],[[[]],[],[]]] => 5
[[[[]]],[[[[]]]]] => [[],[],[[],[],[],[]]] => 6
[[[],[],[]],[],[],[]] => [[[[]]],[[[[]]]]] => 2
[[[[]],[]],[],[],[]] => [[],[[]],[[[[]]]]] => 3
[[[[],[]]],[],[],[]] => [[[]],[],[[[[]]]]] => 3
[[[[[]]]],[],[],[]] => [[],[],[],[[[[]]]]] => 4
[[[[[]]]],[],[[]]] => [[],[],[],[[[],[]]]] => 5
[[[[[]]]],[[],[]]] => [[],[],[],[[[]],[]]] => 5
[[[[[]]]],[[[]]]] => [[],[],[],[[],[],[]]] => 6
[[[],[],[],[]],[],[]] => [[[[[]]]],[[[]]]] => 2
[[[[]],[],[]],[],[]] => [[],[[[]]],[[[]]]] => 3
[[[[],[]],[]],[],[]] => [[[]],[[]],[[[]]]] => 3
[[[[[]]],[]],[],[]] => [[],[],[[]],[[[]]]] => 4
[[[[],[],[]]],[],[]] => [[[[]]],[],[[[]]]] => 3
[[[[[]],[]]],[],[]] => [[],[[]],[],[[[]]]] => 4
[[[[[],[]]]],[],[]] => [[[]],[],[],[[[]]]] => 4
[[[[[[]]]]],[],[]] => [[],[],[],[],[[[]]]] => 5
[[[[[[]]]]],[[]]] => [[],[],[],[],[[],[]]] => 6
[[[],[],[],[],[]],[]] => [[[[[[]]]]],[[]]] => 2
[[[[]],[],[],[]],[]] => [[],[[[[]]]],[[]]] => 3
[[[[],[]],[],[]],[]] => [[[]],[[[]]],[[]]] => 3
[[[[[]]],[],[]],[]] => [[],[],[[[]]],[[]]] => 4
[[[[],[],[]],[]],[]] => [[[[]]],[[]],[[]]] => 3
[[[[[]],[]],[]],[]] => [[],[[]],[[]],[[]]] => 4
[[[[[],[]]],[]],[]] => [[[]],[],[[]],[[]]] => 4
[[[[[[]]]],[]],[]] => [[],[],[],[[]],[[]]] => 5
[[[[],[],[],[]]],[]] => [[[[[]]]],[],[[]]] => 3
[[[[[]],[],[]]],[]] => [[],[[[]]],[],[[]]] => 4
[[[[[],[]],[]]],[]] => [[[]],[[]],[],[[]]] => 4
[[[[[[]]],[]]],[]] => [[],[],[[]],[],[[]]] => 5
[[[[[],[],[]]]],[]] => [[[[]]],[],[],[[]]] => 4
[[[[[[]],[]]]],[]] => [[],[[]],[],[],[[]]] => 5
[[[[[[],[]]]]],[]] => [[[]],[],[],[],[[]]] => 5
[[[[[[[]]]]]],[]] => [[],[],[],[],[],[[]]] => 6
[[[],[],[],[],[],[]]] => [[[[[[[]]]]]],[]] => 2
[[[],[],[],[],[[]]]] => [[[[[[],[]]]]],[]] => 3
[[[],[],[],[[]],[]]] => [[[[[],[[]]]]],[]] => 3
[[[],[],[],[[],[]]]] => [[[[[[]],[]]]],[]] => 3
[[[],[],[],[[[]]]]] => [[[[[],[],[]]]],[]] => 4
[[[],[],[[]],[],[]]] => [[[[],[[[]]]]],[]] => 3
[[[],[],[[]],[[]]]] => [[[[],[[],[]]]],[]] => 4
[[[],[],[[],[]],[]]] => [[[[[]],[[]]]],[]] => 3
[[[],[],[[],[],[]]]] => [[[[[[]]],[]]],[]] => 3
[[[],[],[[],[[]]]]] => [[[[[],[]],[]]],[]] => 4
[[[],[[]],[],[],[]]] => [[[],[[[[]]]]],[]] => 3
[[[],[[],[],[],[]]]] => [[[[[[]]]],[]],[]] => 3
[[[[]],[],[],[],[]]] => [[],[[[[[]]]]],[]] => 3
[[[[],[]],[],[],[]]] => [[[]],[[[[]]]],[]] => 3
[[[[[]]],[],[],[]]] => [[],[],[[[[]]]],[]] => 4
[[[[],[],[]],[],[]]] => [[[[]]],[[[]]],[]] => 3
[[[[[]],[]],[],[]]] => [[],[[]],[[[]]],[]] => 4
[[[[[],[]]],[],[]]] => [[[]],[],[[[]]],[]] => 4
[[[[[[]]]],[],[]]] => [[],[],[],[[[]]],[]] => 5
[[[[],[],[],[]],[]]] => [[[[[]]]],[[]],[]] => 3
[[[[[]],[],[]],[]]] => [[],[[[]]],[[]],[]] => 4
[[[[[],[]],[]],[]]] => [[[]],[[]],[[]],[]] => 4
[[[[[[]]],[]],[]]] => [[],[],[[]],[[]],[]] => 5
[[[[[],[],[]]],[]]] => [[[[]]],[],[[]],[]] => 4
[[[[[[]],[]]],[]]] => [[],[[]],[],[[]],[]] => 5
[[[[[[],[]]]],[]]] => [[[]],[],[],[[]],[]] => 5
[[[[[[[]]]]],[]]] => [[],[],[],[],[[]],[]] => 6
[[[[],[],[],[],[]]]] => [[[[[[]]]]],[],[]] => 3
[[[[[]],[],[],[]]]] => [[],[[[[]]]],[],[]] => 4
[[[[[],[]],[],[]]]] => [[[]],[[[]]],[],[]] => 4
[[[[[[]]],[],[]]]] => [[],[],[[[]]],[],[]] => 5
[[[[[],[],[]],[]]]] => [[[[]]],[[]],[],[]] => 4
[[[[[[]],[]],[]]]] => [[],[[]],[[]],[],[]] => 5
[[[[[[],[]]],[]]]] => [[[]],[],[[]],[],[]] => 5
[[[[[[[]]]],[]]]] => [[],[],[],[[]],[],[]] => 6
[[[[[],[],[],[]]]]] => [[[[[]]]],[],[],[]] => 4
[[[[[[]],[],[]]]]] => [[],[[[]]],[],[],[]] => 5
[[[[[[],[]],[]]]]] => [[[]],[[]],[],[],[]] => 5
[[[[[[[]]],[]]]]] => [[],[],[[]],[],[],[]] => 6
[[[[[[],[],[]]]]]] => [[[[]]],[],[],[],[]] => 5
[[[[[[[]],[]]]]]] => [[],[[]],[],[],[],[]] => 6
[[[[[[[],[]]]]]]] => [[[]],[],[],[],[],[]] => 6
[[[[[[[[]]]]]]]] => [[],[],[],[],[],[],[]] => 7
[[],[[[[[],[],[]]]]]] => [[[[[]]],[],[],[],[]]] => 5
[[],[[[[[],[[]]]]]]] => [[[[],[]],[],[],[],[]]] => 6
[[],[[[[[[],[]]]]]]] => [[[[]],[],[],[],[],[]]] => 6
[[],[[[[[[[]]]]]]]] => [[[],[],[],[],[],[],[]]] => 7
[[[]],[],[],[],[],[],[]] => [[],[[[[[[[]]]]]]]] => 2
[[[]],[],[],[],[],[[]]] => [[],[[[[[[],[]]]]]]] => 3
[[[]],[],[],[],[[]],[]] => [[],[[[[[],[[]]]]]]] => 3
[[[]],[],[],[],[[],[]]] => [[],[[[[[[]],[]]]]]] => 3
[[[]],[],[],[],[[[]]]] => [[],[[[[[],[],[]]]]]] => 4
[[[]],[],[],[[]],[],[]] => [[],[[[[],[[[]]]]]]] => 3
[[[]],[],[],[[],[],[]]] => [[],[[[[[[]]],[]]]]] => 3
[[[]],[[]],[[]],[[]]] => [[],[[],[[],[[],[]]]]] => 5
[[[]],[[]],[[],[[]]]] => [[],[[],[[[],[]],[]]]] => 5
[[[]],[[],[[]]],[[]]] => [[],[[[],[]],[[],[]]]] => 5
[[[]],[[],[[]],[[]]]] => [[],[[[],[[],[]]],[]]] => 5
[[[]],[[],[[],[[]]]]] => [[],[[[[],[]],[]],[]]] => 5
[[[]],[[[[],[],[]]]]] => [[],[[[[]]],[],[],[]]] => 5
[[[]],[[[[],[[]]]]]] => [[],[[[],[]],[],[],[]]] => 6
[[[]],[[[[[],[]]]]]] => [[],[[[]],[],[],[],[]]] => 6
[[[]],[[[[[[]]]]]]] => [[],[[],[],[],[],[],[]]] => 7
[[[[]]],[[[],[],[]]]] => [[],[],[[[[]]],[],[]]] => 5
[[[[]]],[[[],[[]]]]] => [[],[],[[[],[]],[],[]]] => 6
[[[[]]],[[[[],[]]]]] => [[],[],[[[]],[],[],[]]] => 6
[[[[]]],[[[[[]]]]]] => [[],[],[[],[],[],[],[]]] => 7
[[[],[[]]],[[]],[[]]] => [[[],[]],[[],[[],[]]]] => 5
[[[],[[]]],[[],[[]]]] => [[[],[]],[[[],[]],[]]] => 5
[[[[[]]]],[[],[],[]]] => [[],[],[],[[[[]]],[]]] => 5
[[[[[]]]],[[],[[]]]] => [[],[],[],[[[],[]],[]]] => 6
[[[[[]]]],[[[],[]]]] => [[],[],[],[[[]],[],[]]] => 6
[[[[[]]]],[[[[]]]]] => [[],[],[],[[],[],[],[]]] => 7
[[[[[[]]]]],[],[],[]] => [[],[],[],[],[[[[]]]]] => 5
[[[[[[]]]]],[],[[]]] => [[],[],[],[],[[[],[]]]] => 6
[[[[[[]]]]],[[],[]]] => [[],[],[],[],[[[]],[]]] => 6
[[[[[[]]]]],[[[]]]] => [[],[],[],[],[[],[],[]]] => 7
[[[[[[[]]]]]],[],[]] => [[],[],[],[],[],[[[]]]] => 6
[[[],[[]],[[]]],[[]]] => [[[],[[],[]]],[[],[]]] => 5
[[[],[[],[[]]]],[[]]] => [[[[],[]],[]],[[],[]]] => 5
[[[[[[[]]]]]],[[]]] => [[],[],[],[],[],[[],[]]] => 7
[[[[[[[[]]]]]]],[]] => [[],[],[],[],[],[],[[]]] => 7
[[[],[],[],[],[],[],[]]] => [[[[[[[[]]]]]]],[]] => 2
[[[],[],[],[],[],[[]]]] => [[[[[[[],[]]]]]],[]] => 3
[[[],[],[],[],[[]],[]]] => [[[[[[],[[]]]]]],[]] => 3
[[[],[],[],[],[[],[]]]] => [[[[[[[]],[]]]]],[]] => 3
[[[],[],[],[],[[[]]]]] => [[[[[[],[],[]]]]],[]] => 4
[[[],[],[],[[]],[],[]]] => [[[[[],[[[]]]]]],[]] => 3
[[[],[],[],[[],[],[]]]] => [[[[[[[]]],[]]]],[]] => 3
[[[],[[]],[[]],[[]]]] => [[[],[[],[[],[]]]],[]] => 5
[[[],[[]],[[],[[]]]]] => [[[],[[[],[]],[]]],[]] => 5
[[[],[[],[[]]],[[]]]] => [[[[],[]],[[],[]]],[]] => 5
[[[],[[],[[]],[[]]]]] => [[[[],[[],[]]],[]],[]] => 5
[[[],[[],[[],[[]]]]]] => [[[[[],[]],[]],[]],[]] => 5
[[[[[[[[[]]]]]]]]] => [[],[],[],[],[],[],[],[]] => 8
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
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Description
The number of leaves of an ordered tree.
This is the number of nodes which do not have any children.
Map
DeBruijn-Morselt plane tree automorphism
Description
This automorphism on the set of plane trees with a given number of vertices is the combination of the two "canonical" bijections between plane trees and binary trees, using either the left or right branches. In [3] Shapiro essentially attributes this automorphism to DeBruijn and Morselt [1], hence the name I chose. Shapiro shows in that paper that for a large subset of plane trees (those corresponding to compositions), the sixth power of the automorphism acts as the identity on this subset. However, its behavior in general is quite chaotic. In [2] Donaghey studies this automorphism further and shows that its behavior on all trees can be reduced to its behavior on certain "primitive" trees.