Identifier
Values
[[]] => [.,.] => [1,0] => 10 => 1
[[],[]] => [[.,.],.] => [1,1,0,0] => 1100 => 2
[[[]]] => [.,[.,.]] => [1,0,1,0] => 1010 => 1
[[],[],[]] => [[[.,.],.],.] => [1,1,1,0,0,0] => 111000 => 3
[[],[[]]] => [[.,.],[.,.]] => [1,1,0,0,1,0] => 110010 => 2
[[[]],[]] => [[.,[.,.]],.] => [1,1,0,1,0,0] => 110100 => 2
[[[],[]]] => [.,[[.,.],.]] => [1,0,1,1,0,0] => 101100 => 2
[[[[]]]] => [.,[.,[.,.]]] => [1,0,1,0,1,0] => 101010 => 1
[[],[],[],[]] => [[[[.,.],.],.],.] => [1,1,1,1,0,0,0,0] => 11110000 => 4
[[],[],[[]]] => [[[.,.],.],[.,.]] => [1,1,1,0,0,0,1,0] => 11100010 => 3
[[],[[]],[]] => [[[.,.],[.,.]],.] => [1,1,1,0,0,1,0,0] => 11100100 => 3
[[],[[],[]]] => [[.,.],[[.,.],.]] => [1,1,0,0,1,1,0,0] => 11001100 => 2
[[],[[[]]]] => [[.,.],[.,[.,.]]] => [1,1,0,0,1,0,1,0] => 11001010 => 2
[[[]],[],[]] => [[[.,[.,.]],.],.] => [1,1,1,0,1,0,0,0] => 11101000 => 3
[[[]],[[]]] => [[.,[.,.]],[.,.]] => [1,1,0,1,0,0,1,0] => 11010010 => 2
[[[],[]],[]] => [[.,[[.,.],.]],.] => [1,1,0,1,1,0,0,0] => 11011000 => 2
[[[[]]],[]] => [[.,[.,[.,.]]],.] => [1,1,0,1,0,1,0,0] => 11010100 => 2
[[[],[],[]]] => [.,[[[.,.],.],.]] => [1,0,1,1,1,0,0,0] => 10111000 => 3
[[[],[[]]]] => [.,[[.,.],[.,.]]] => [1,0,1,1,0,0,1,0] => 10110010 => 2
[[[[]],[]]] => [.,[[.,[.,.]],.]] => [1,0,1,1,0,1,0,0] => 10110100 => 2
[[[[],[]]]] => [.,[.,[[.,.],.]]] => [1,0,1,0,1,1,0,0] => 10101100 => 2
[[[[[]]]]] => [.,[.,[.,[.,.]]]] => [1,0,1,0,1,0,1,0] => 10101010 => 1
[[],[],[],[],[]] => [[[[[.,.],.],.],.],.] => [1,1,1,1,1,0,0,0,0,0] => 1111100000 => 5
[[],[],[],[[]]] => [[[[.,.],.],.],[.,.]] => [1,1,1,1,0,0,0,0,1,0] => 1111000010 => 4
[[],[],[[]],[]] => [[[[.,.],.],[.,.]],.] => [1,1,1,1,0,0,0,1,0,0] => 1111000100 => 4
[[],[],[[],[]]] => [[[.,.],.],[[.,.],.]] => [1,1,1,0,0,0,1,1,0,0] => 1110001100 => 3
[[],[],[[[]]]] => [[[.,.],.],[.,[.,.]]] => [1,1,1,0,0,0,1,0,1,0] => 1110001010 => 3
[[],[[]],[],[]] => [[[[.,.],[.,.]],.],.] => [1,1,1,1,0,0,1,0,0,0] => 1111001000 => 4
[[],[[]],[[]]] => [[[.,.],[.,.]],[.,.]] => [1,1,1,0,0,1,0,0,1,0] => 1110010010 => 3
[[],[[],[]],[]] => [[[.,.],[[.,.],.]],.] => [1,1,1,0,0,1,1,0,0,0] => 1110011000 => 3
[[],[[[]]],[]] => [[[.,.],[.,[.,.]]],.] => [1,1,1,0,0,1,0,1,0,0] => 1110010100 => 3
[[],[[],[],[]]] => [[.,.],[[[.,.],.],.]] => [1,1,0,0,1,1,1,0,0,0] => 1100111000 => 3
[[],[[],[[]]]] => [[.,.],[[.,.],[.,.]]] => [1,1,0,0,1,1,0,0,1,0] => 1100110010 => 2
[[],[[[]],[]]] => [[.,.],[[.,[.,.]],.]] => [1,1,0,0,1,1,0,1,0,0] => 1100110100 => 2
[[],[[[],[]]]] => [[.,.],[.,[[.,.],.]]] => [1,1,0,0,1,0,1,1,0,0] => 1100101100 => 2
[[],[[[[]]]]] => [[.,.],[.,[.,[.,.]]]] => [1,1,0,0,1,0,1,0,1,0] => 1100101010 => 2
[[[]],[],[],[]] => [[[[.,[.,.]],.],.],.] => [1,1,1,1,0,1,0,0,0,0] => 1111010000 => 4
[[[]],[],[[]]] => [[[.,[.,.]],.],[.,.]] => [1,1,1,0,1,0,0,0,1,0] => 1110100010 => 3
[[[]],[[]],[]] => [[[.,[.,.]],[.,.]],.] => [1,1,1,0,1,0,0,1,0,0] => 1110100100 => 3
[[[]],[[],[]]] => [[.,[.,.]],[[.,.],.]] => [1,1,0,1,0,0,1,1,0,0] => 1101001100 => 2
[[[]],[[[]]]] => [[.,[.,.]],[.,[.,.]]] => [1,1,0,1,0,0,1,0,1,0] => 1101001010 => 2
[[[],[]],[],[]] => [[[.,[[.,.],.]],.],.] => [1,1,1,0,1,1,0,0,0,0] => 1110110000 => 3
[[[[]]],[],[]] => [[[.,[.,[.,.]]],.],.] => [1,1,1,0,1,0,1,0,0,0] => 1110101000 => 3
[[[],[]],[[]]] => [[.,[[.,.],.]],[.,.]] => [1,1,0,1,1,0,0,0,1,0] => 1101100010 => 2
[[[[]]],[[]]] => [[.,[.,[.,.]]],[.,.]] => [1,1,0,1,0,1,0,0,1,0] => 1101010010 => 2
[[[],[],[]],[]] => [[.,[[[.,.],.],.]],.] => [1,1,0,1,1,1,0,0,0,0] => 1101110000 => 3
[[[],[[]]],[]] => [[.,[[.,.],[.,.]]],.] => [1,1,0,1,1,0,0,1,0,0] => 1101100100 => 2
[[[[]],[]],[]] => [[.,[[.,[.,.]],.]],.] => [1,1,0,1,1,0,1,0,0,0] => 1101101000 => 2
[[[[],[]]],[]] => [[.,[.,[[.,.],.]]],.] => [1,1,0,1,0,1,1,0,0,0] => 1101011000 => 2
[[[[[]]]],[]] => [[.,[.,[.,[.,.]]]],.] => [1,1,0,1,0,1,0,1,0,0] => 1101010100 => 2
[[[],[],[],[]]] => [.,[[[[.,.],.],.],.]] => [1,0,1,1,1,1,0,0,0,0] => 1011110000 => 4
[[[],[],[[]]]] => [.,[[[.,.],.],[.,.]]] => [1,0,1,1,1,0,0,0,1,0] => 1011100010 => 3
[[[],[[]],[]]] => [.,[[[.,.],[.,.]],.]] => [1,0,1,1,1,0,0,1,0,0] => 1011100100 => 3
[[[],[[],[]]]] => [.,[[.,.],[[.,.],.]]] => [1,0,1,1,0,0,1,1,0,0] => 1011001100 => 2
[[[],[[[]]]]] => [.,[[.,.],[.,[.,.]]]] => [1,0,1,1,0,0,1,0,1,0] => 1011001010 => 2
[[[[]],[],[]]] => [.,[[[.,[.,.]],.],.]] => [1,0,1,1,1,0,1,0,0,0] => 1011101000 => 3
[[[[]],[[]]]] => [.,[[.,[.,.]],[.,.]]] => [1,0,1,1,0,1,0,0,1,0] => 1011010010 => 2
[[[[],[]],[]]] => [.,[[.,[[.,.],.]],.]] => [1,0,1,1,0,1,1,0,0,0] => 1011011000 => 2
[[[[[]]],[]]] => [.,[[.,[.,[.,.]]],.]] => [1,0,1,1,0,1,0,1,0,0] => 1011010100 => 2
[[[[],[],[]]]] => [.,[.,[[[.,.],.],.]]] => [1,0,1,0,1,1,1,0,0,0] => 1010111000 => 3
[[[[],[[]]]]] => [.,[.,[[.,.],[.,.]]]] => [1,0,1,0,1,1,0,0,1,0] => 1010110010 => 2
[[[[[]],[]]]] => [.,[.,[[.,[.,.]],.]]] => [1,0,1,0,1,1,0,1,0,0] => 1010110100 => 2
[[[[[],[]]]]] => [.,[.,[.,[[.,.],.]]]] => [1,0,1,0,1,0,1,1,0,0] => 1010101100 => 2
[[[[[[]]]]]] => [.,[.,[.,[.,[.,.]]]]] => [1,0,1,0,1,0,1,0,1,0] => 1010101010 => 1
[[],[],[],[],[],[]] => [[[[[[.,.],.],.],.],.],.] => [1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 6
[[],[],[],[],[[]]] => [[[[[.,.],.],.],.],[.,.]] => [1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 5
[[],[],[],[[]],[]] => [[[[[.,.],.],.],[.,.]],.] => [1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 5
[[],[],[],[[],[]]] => [[[[.,.],.],.],[[.,.],.]] => [1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 4
[[],[],[],[[[]]]] => [[[[.,.],.],.],[.,[.,.]]] => [1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 4
[[],[],[[]],[],[]] => [[[[[.,.],.],[.,.]],.],.] => [1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 5
[[],[],[[]],[[]]] => [[[[.,.],.],[.,.]],[.,.]] => [1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 4
[[],[],[[],[]],[]] => [[[[.,.],.],[[.,.],.]],.] => [1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 4
[[],[],[[[]]],[]] => [[[[.,.],.],[.,[.,.]]],.] => [1,1,1,1,0,0,0,1,0,1,0,0] => 111100010100 => 4
[[],[],[[],[],[]]] => [[[.,.],.],[[[.,.],.],.]] => [1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 3
[[],[],[[],[[]]]] => [[[.,.],.],[[.,.],[.,.]]] => [1,1,1,0,0,0,1,1,0,0,1,0] => 111000110010 => 3
[[],[],[[[]],[]]] => [[[.,.],.],[[.,[.,.]],.]] => [1,1,1,0,0,0,1,1,0,1,0,0] => 111000110100 => 3
[[],[],[[[],[]]]] => [[[.,.],.],[.,[[.,.],.]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => 111000101100 => 3
[[],[],[[[[]]]]] => [[[.,.],.],[.,[.,[.,.]]]] => [1,1,1,0,0,0,1,0,1,0,1,0] => 111000101010 => 3
[[],[[]],[],[],[]] => [[[[[.,.],[.,.]],.],.],.] => [1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 5
[[],[[]],[],[[]]] => [[[[.,.],[.,.]],.],[.,.]] => [1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 4
[[],[[]],[[]],[]] => [[[[.,.],[.,.]],[.,.]],.] => [1,1,1,1,0,0,1,0,0,1,0,0] => 111100100100 => 4
[[],[[]],[[],[]]] => [[[.,.],[.,.]],[[.,.],.]] => [1,1,1,0,0,1,0,0,1,1,0,0] => 111001001100 => 3
[[],[[]],[[[]]]] => [[[.,.],[.,.]],[.,[.,.]]] => [1,1,1,0,0,1,0,0,1,0,1,0] => 111001001010 => 3
[[],[[],[]],[],[]] => [[[[.,.],[[.,.],.]],.],.] => [1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 4
[[],[[[]]],[],[]] => [[[[.,.],[.,[.,.]]],.],.] => [1,1,1,1,0,0,1,0,1,0,0,0] => 111100101000 => 4
[[],[[],[]],[[]]] => [[[.,.],[[.,.],.]],[.,.]] => [1,1,1,0,0,1,1,0,0,0,1,0] => 111001100010 => 3
[[],[[[]]],[[]]] => [[[.,.],[.,[.,.]]],[.,.]] => [1,1,1,0,0,1,0,1,0,0,1,0] => 111001010010 => 3
[[],[[],[],[]],[]] => [[[.,.],[[[.,.],.],.]],.] => [1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 3
[[],[[],[[]]],[]] => [[[.,.],[[.,.],[.,.]]],.] => [1,1,1,0,0,1,1,0,0,1,0,0] => 111001100100 => 3
[[],[[[]],[]],[]] => [[[.,.],[[.,[.,.]],.]],.] => [1,1,1,0,0,1,1,0,1,0,0,0] => 111001101000 => 3
[[],[[[],[]]],[]] => [[[.,.],[.,[[.,.],.]]],.] => [1,1,1,0,0,1,0,1,1,0,0,0] => 111001011000 => 3
[[],[[[[]]]],[]] => [[[.,.],[.,[.,[.,.]]]],.] => [1,1,1,0,0,1,0,1,0,1,0,0] => 111001010100 => 3
[[],[[],[],[],[]]] => [[.,.],[[[[.,.],.],.],.]] => [1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 4
[[],[[],[],[[]]]] => [[.,.],[[[.,.],.],[.,.]]] => [1,1,0,0,1,1,1,0,0,0,1,0] => 110011100010 => 3
[[],[[],[[]],[]]] => [[.,.],[[[.,.],[.,.]],.]] => [1,1,0,0,1,1,1,0,0,1,0,0] => 110011100100 => 3
[[],[[],[[],[]]]] => [[.,.],[[.,.],[[.,.],.]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => 110011001100 => 2
[[],[[],[[[]]]]] => [[.,.],[[.,.],[.,[.,.]]]] => [1,1,0,0,1,1,0,0,1,0,1,0] => 110011001010 => 2
[[],[[[]],[],[]]] => [[.,.],[[[.,[.,.]],.],.]] => [1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => 3
[[],[[[]],[[]]]] => [[.,.],[[.,[.,.]],[.,.]]] => [1,1,0,0,1,1,0,1,0,0,1,0] => 110011010010 => 2
[[],[[[],[]],[]]] => [[.,.],[[.,[[.,.],.]],.]] => [1,1,0,0,1,1,0,1,1,0,0,0] => 110011011000 => 2
[[],[[[[]]],[]]] => [[.,.],[[.,[.,[.,.]]],.]] => [1,1,0,0,1,1,0,1,0,1,0,0] => 110011010100 => 2
>>> Load all 236 entries. <<<
[[],[[[],[],[]]]] => [[.,.],[.,[[[.,.],.],.]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => 110010111000 => 3
[[],[[[],[[]]]]] => [[.,.],[.,[[.,.],[.,.]]]] => [1,1,0,0,1,0,1,1,0,0,1,0] => 110010110010 => 2
[[],[[[[]],[]]]] => [[.,.],[.,[[.,[.,.]],.]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => 2
[[],[[[[],[]]]]] => [[.,.],[.,[.,[[.,.],.]]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => 110010101100 => 2
[[],[[[[[]]]]]] => [[.,.],[.,[.,[.,[.,.]]]]] => [1,1,0,0,1,0,1,0,1,0,1,0] => 110010101010 => 2
[[[]],[],[],[],[]] => [[[[[.,[.,.]],.],.],.],.] => [1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 5
[[[]],[],[],[[]]] => [[[[.,[.,.]],.],.],[.,.]] => [1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 4
[[[]],[],[[]],[]] => [[[[.,[.,.]],.],[.,.]],.] => [1,1,1,1,0,1,0,0,0,1,0,0] => 111101000100 => 4
[[[]],[],[[],[]]] => [[[.,[.,.]],.],[[.,.],.]] => [1,1,1,0,1,0,0,0,1,1,0,0] => 111010001100 => 3
[[[]],[],[[[]]]] => [[[.,[.,.]],.],[.,[.,.]]] => [1,1,1,0,1,0,0,0,1,0,1,0] => 111010001010 => 3
[[[]],[[]],[],[]] => [[[[.,[.,.]],[.,.]],.],.] => [1,1,1,1,0,1,0,0,1,0,0,0] => 111101001000 => 4
[[[]],[[]],[[]]] => [[[.,[.,.]],[.,.]],[.,.]] => [1,1,1,0,1,0,0,1,0,0,1,0] => 111010010010 => 3
[[[]],[[],[]],[]] => [[[.,[.,.]],[[.,.],.]],.] => [1,1,1,0,1,0,0,1,1,0,0,0] => 111010011000 => 3
[[[]],[[[]]],[]] => [[[.,[.,.]],[.,[.,.]]],.] => [1,1,1,0,1,0,0,1,0,1,0,0] => 111010010100 => 3
[[[]],[[],[],[]]] => [[.,[.,.]],[[[.,.],.],.]] => [1,1,0,1,0,0,1,1,1,0,0,0] => 110100111000 => 3
[[[]],[[],[[]]]] => [[.,[.,.]],[[.,.],[.,.]]] => [1,1,0,1,0,0,1,1,0,0,1,0] => 110100110010 => 2
[[[]],[[[]],[]]] => [[.,[.,.]],[[.,[.,.]],.]] => [1,1,0,1,0,0,1,1,0,1,0,0] => 110100110100 => 2
[[[]],[[[],[]]]] => [[.,[.,.]],[.,[[.,.],.]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => 110100101100 => 2
[[[]],[[[[]]]]] => [[.,[.,.]],[.,[.,[.,.]]]] => [1,1,0,1,0,0,1,0,1,0,1,0] => 110100101010 => 2
[[[],[]],[],[],[]] => [[[[.,[[.,.],.]],.],.],.] => [1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 4
[[[[]]],[],[],[]] => [[[[.,[.,[.,.]]],.],.],.] => [1,1,1,1,0,1,0,1,0,0,0,0] => 111101010000 => 4
[[[],[]],[],[[]]] => [[[.,[[.,.],.]],.],[.,.]] => [1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 3
[[[[]]],[],[[]]] => [[[.,[.,[.,.]]],.],[.,.]] => [1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => 3
[[[],[]],[[]],[]] => [[[.,[[.,.],.]],[.,.]],.] => [1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => 3
[[[[]]],[[]],[]] => [[[.,[.,[.,.]]],[.,.]],.] => [1,1,1,0,1,0,1,0,0,1,0,0] => 111010100100 => 3
[[[],[]],[[],[]]] => [[.,[[.,.],.]],[[.,.],.]] => [1,1,0,1,1,0,0,0,1,1,0,0] => 110110001100 => 2
[[[],[]],[[[]]]] => [[.,[[.,.],.]],[.,[.,.]]] => [1,1,0,1,1,0,0,0,1,0,1,0] => 110110001010 => 2
[[[[]]],[[],[]]] => [[.,[.,[.,.]]],[[.,.],.]] => [1,1,0,1,0,1,0,0,1,1,0,0] => 110101001100 => 2
[[[[]]],[[[]]]] => [[.,[.,[.,.]]],[.,[.,.]]] => [1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => 2
[[[],[],[]],[],[]] => [[[.,[[[.,.],.],.]],.],.] => [1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 3
[[[],[[]]],[],[]] => [[[.,[[.,.],[.,.]]],.],.] => [1,1,1,0,1,1,0,0,1,0,0,0] => 111011001000 => 3
[[[[]],[]],[],[]] => [[[.,[[.,[.,.]],.]],.],.] => [1,1,1,0,1,1,0,1,0,0,0,0] => 111011010000 => 3
[[[[],[]]],[],[]] => [[[.,[.,[[.,.],.]]],.],.] => [1,1,1,0,1,0,1,1,0,0,0,0] => 111010110000 => 3
[[[[[]]]],[],[]] => [[[.,[.,[.,[.,.]]]],.],.] => [1,1,1,0,1,0,1,0,1,0,0,0] => 111010101000 => 3
[[[],[],[]],[[]]] => [[.,[[[.,.],.],.]],[.,.]] => [1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 3
[[[],[[]]],[[]]] => [[.,[[.,.],[.,.]]],[.,.]] => [1,1,0,1,1,0,0,1,0,0,1,0] => 110110010010 => 2
[[[[]],[]],[[]]] => [[.,[[.,[.,.]],.]],[.,.]] => [1,1,0,1,1,0,1,0,0,0,1,0] => 110110100010 => 2
[[[[],[]]],[[]]] => [[.,[.,[[.,.],.]]],[.,.]] => [1,1,0,1,0,1,1,0,0,0,1,0] => 110101100010 => 2
[[[[[]]]],[[]]] => [[.,[.,[.,[.,.]]]],[.,.]] => [1,1,0,1,0,1,0,1,0,0,1,0] => 110101010010 => 2
[[[],[],[],[]],[]] => [[.,[[[[.,.],.],.],.]],.] => [1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 4
[[[],[],[[]]],[]] => [[.,[[[.,.],.],[.,.]]],.] => [1,1,0,1,1,1,0,0,0,1,0,0] => 110111000100 => 3
[[[],[[]],[]],[]] => [[.,[[[.,.],[.,.]],.]],.] => [1,1,0,1,1,1,0,0,1,0,0,0] => 110111001000 => 3
[[[],[[],[]]],[]] => [[.,[[.,.],[[.,.],.]]],.] => [1,1,0,1,1,0,0,1,1,0,0,0] => 110110011000 => 2
[[[],[[[]]]],[]] => [[.,[[.,.],[.,[.,.]]]],.] => [1,1,0,1,1,0,0,1,0,1,0,0] => 110110010100 => 2
[[[[]],[],[]],[]] => [[.,[[[.,[.,.]],.],.]],.] => [1,1,0,1,1,1,0,1,0,0,0,0] => 110111010000 => 3
[[[[]],[[]]],[]] => [[.,[[.,[.,.]],[.,.]]],.] => [1,1,0,1,1,0,1,0,0,1,0,0] => 110110100100 => 2
[[[[],[]],[]],[]] => [[.,[[.,[[.,.],.]],.]],.] => [1,1,0,1,1,0,1,1,0,0,0,0] => 110110110000 => 2
[[[[[]]],[]],[]] => [[.,[[.,[.,[.,.]]],.]],.] => [1,1,0,1,1,0,1,0,1,0,0,0] => 110110101000 => 2
[[[[],[],[]]],[]] => [[.,[.,[[[.,.],.],.]]],.] => [1,1,0,1,0,1,1,1,0,0,0,0] => 110101110000 => 3
[[[[],[[]]]],[]] => [[.,[.,[[.,.],[.,.]]]],.] => [1,1,0,1,0,1,1,0,0,1,0,0] => 110101100100 => 2
[[[[[]],[]]],[]] => [[.,[.,[[.,[.,.]],.]]],.] => [1,1,0,1,0,1,1,0,1,0,0,0] => 110101101000 => 2
[[[[[],[]]]],[]] => [[.,[.,[.,[[.,.],.]]]],.] => [1,1,0,1,0,1,0,1,1,0,0,0] => 110101011000 => 2
[[[[[[]]]]],[]] => [[.,[.,[.,[.,[.,.]]]]],.] => [1,1,0,1,0,1,0,1,0,1,0,0] => 110101010100 => 2
[[[],[],[],[],[]]] => [.,[[[[[.,.],.],.],.],.]] => [1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 5
[[[],[],[],[[]]]] => [.,[[[[.,.],.],.],[.,.]]] => [1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 4
[[[],[],[[]],[]]] => [.,[[[[.,.],.],[.,.]],.]] => [1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 4
[[[],[],[[],[]]]] => [.,[[[.,.],.],[[.,.],.]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => 101110001100 => 3
[[[],[],[[[]]]]] => [.,[[[.,.],.],[.,[.,.]]]] => [1,0,1,1,1,0,0,0,1,0,1,0] => 101110001010 => 3
[[[],[[]],[],[]]] => [.,[[[[.,.],[.,.]],.],.]] => [1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 4
[[[],[[]],[[]]]] => [.,[[[.,.],[.,.]],[.,.]]] => [1,0,1,1,1,0,0,1,0,0,1,0] => 101110010010 => 3
[[[],[[],[]],[]]] => [.,[[[.,.],[[.,.],.]],.]] => [1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 3
[[[],[[[]]],[]]] => [.,[[[.,.],[.,[.,.]]],.]] => [1,0,1,1,1,0,0,1,0,1,0,0] => 101110010100 => 3
[[[],[[],[],[]]]] => [.,[[.,.],[[[.,.],.],.]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => 101100111000 => 3
[[[],[[],[[]]]]] => [.,[[.,.],[[.,.],[.,.]]]] => [1,0,1,1,0,0,1,1,0,0,1,0] => 101100110010 => 2
[[[],[[[]],[]]]] => [.,[[.,.],[[.,[.,.]],.]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => 101100110100 => 2
[[[],[[[],[]]]]] => [.,[[.,.],[.,[[.,.],.]]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => 101100101100 => 2
[[[],[[[[]]]]]] => [.,[[.,.],[.,[.,[.,.]]]]] => [1,0,1,1,0,0,1,0,1,0,1,0] => 101100101010 => 2
[[[[]],[],[],[]]] => [.,[[[[.,[.,.]],.],.],.]] => [1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 4
[[[[]],[],[[]]]] => [.,[[[.,[.,.]],.],[.,.]]] => [1,0,1,1,1,0,1,0,0,0,1,0] => 101110100010 => 3
[[[[]],[[]],[]]] => [.,[[[.,[.,.]],[.,.]],.]] => [1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => 3
[[[[]],[[],[]]]] => [.,[[.,[.,.]],[[.,.],.]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => 101101001100 => 2
[[[[]],[[[]]]]] => [.,[[.,[.,.]],[.,[.,.]]]] => [1,0,1,1,0,1,0,0,1,0,1,0] => 101101001010 => 2
[[[[],[]],[],[]]] => [.,[[[.,[[.,.],.]],.],.]] => [1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 3
[[[[[]]],[],[]]] => [.,[[[.,[.,[.,.]]],.],.]] => [1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 3
[[[[],[]],[[]]]] => [.,[[.,[[.,.],.]],[.,.]]] => [1,0,1,1,0,1,1,0,0,0,1,0] => 101101100010 => 2
[[[[[]]],[[]]]] => [.,[[.,[.,[.,.]]],[.,.]]] => [1,0,1,1,0,1,0,1,0,0,1,0] => 101101010010 => 2
[[[[],[],[]],[]]] => [.,[[.,[[[.,.],.],.]],.]] => [1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 3
[[[[],[[]]],[]]] => [.,[[.,[[.,.],[.,.]]],.]] => [1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => 2
[[[[[]],[]],[]]] => [.,[[.,[[.,[.,.]],.]],.]] => [1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 2
[[[[[],[]]],[]]] => [.,[[.,[.,[[.,.],.]]],.]] => [1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 2
[[[[[[]]]],[]]] => [.,[[.,[.,[.,[.,.]]]],.]] => [1,0,1,1,0,1,0,1,0,1,0,0] => 101101010100 => 2
[[[[],[],[],[]]]] => [.,[.,[[[[.,.],.],.],.]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 4
[[[[],[],[[]]]]] => [.,[.,[[[.,.],.],[.,.]]]] => [1,0,1,0,1,1,1,0,0,0,1,0] => 101011100010 => 3
[[[[],[[]],[]]]] => [.,[.,[[[.,.],[.,.]],.]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => 101011100100 => 3
[[[[],[[],[]]]]] => [.,[.,[[.,.],[[.,.],.]]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => 101011001100 => 2
[[[[],[[[]]]]]] => [.,[.,[[.,.],[.,[.,.]]]]] => [1,0,1,0,1,1,0,0,1,0,1,0] => 101011001010 => 2
[[[[[]],[],[]]]] => [.,[.,[[[.,[.,.]],.],.]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => 3
[[[[[]],[[]]]]] => [.,[.,[[.,[.,.]],[.,.]]]] => [1,0,1,0,1,1,0,1,0,0,1,0] => 101011010010 => 2
[[[[[],[]],[]]]] => [.,[.,[[.,[[.,.],.]],.]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => 101011011000 => 2
[[[[[[]]],[]]]] => [.,[.,[[.,[.,[.,.]]],.]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => 101011010100 => 2
[[[[[],[],[]]]]] => [.,[.,[.,[[[.,.],.],.]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => 101010111000 => 3
[[[[[],[[]]]]]] => [.,[.,[.,[[.,.],[.,.]]]]] => [1,0,1,0,1,0,1,1,0,0,1,0] => 101010110010 => 2
[[[[[[]],[]]]]] => [.,[.,[.,[[.,[.,.]],.]]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => 101010110100 => 2
[[[[[[],[]]]]]] => [.,[.,[.,[.,[[.,.],.]]]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => 101010101100 => 2
[[[[[[[]]]]]]] => [.,[.,[.,[.,[.,[.,.]]]]]] => [1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => 1
[[],[],[],[],[],[[]]] => [[[[[[.,.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 6
[[],[],[],[],[[],[]]] => [[[[[.,.],.],.],.],[[.,.],.]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 5
[[],[],[],[[]],[[]]] => [[[[[.,.],.],.],[.,.]],[.,.]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 5
[[],[],[[]],[],[[]]] => [[[[[.,.],.],[.,.]],.],[.,.]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 5
[[],[[]],[],[],[[]]] => [[[[[.,.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 5
[[],[[],[]],[],[[]]] => [[[[.,.],[[.,.],.]],.],[.,.]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 4
[[],[[],[],[],[],[]]] => [[.,.],[[[[[.,.],.],.],.],.]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 5
[[[]],[],[],[],[[]]] => [[[[[.,[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 5
[[[]],[[]],[],[[]]] => [[[[.,[.,.]],[.,.]],.],[.,.]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11110100100010 => 4
[[[],[]],[],[],[[]]] => [[[[.,[[.,.],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 4
[[[[]]],[],[],[[]]] => [[[[.,[.,[.,.]]],.],.],[.,.]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11110101000010 => 4
[[[],[],[]],[],[[]]] => [[[.,[[[.,.],.],.]],.],[.,.]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 3
[[[[]],[]],[],[[]]] => [[[.,[[.,[.,.]],.]],.],[.,.]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11101101000010 => 3
[[[],[],[],[]],[[]]] => [[.,[[[[.,.],.],.],.]],[.,.]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 4
[[[],[],[],[],[],[]]] => [.,[[[[[[.,.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 6
[[[],[],[],[[]],[]]] => [.,[[[[[.,.],.],.],[.,.]],.]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 5
[[[],[],[[]],[],[]]] => [.,[[[[[.,.],.],[.,.]],.],.]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 5
[[[],[[]],[],[],[]]] => [.,[[[[[.,.],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 5
[[[],[[],[]],[],[]]] => [.,[[[[.,.],[[.,.],.]],.],.]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 4
[[[[]],[],[],[],[]]] => [.,[[[[[.,[.,.]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 5
[[[[]],[[]],[],[]]] => [.,[[[[.,[.,.]],[.,.]],.],.]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 10111101001000 => 4
[[[[],[]],[],[],[]]] => [.,[[[[.,[[.,.],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 4
[[[[[]]],[],[],[]]] => [.,[[[[.,[.,[.,.]]],.],.],.]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 4
[[[[],[],[]],[],[]]] => [.,[[[.,[[[.,.],.],.]],.],.]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 3
[[[[[]],[]],[],[]]] => [.,[[[.,[[.,[.,.]],.]],.],.]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => 3
[[[[],[],[],[]],[]]] => [.,[[.,[[[[.,.],.],.],.]],.]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 4
[[],[],[],[],[],[],[[]]] => [[[[[[[.,.],.],.],.],.],.],[.,.]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 7
[[],[],[[]],[],[],[[]]] => [[[[[[.,.],.],[.,.]],.],.],[.,.]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 6
[[],[[]],[],[],[],[[]]] => [[[[[[.,.],[.,.]],.],.],.],[.,.]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 6
[[[]],[],[],[],[],[[]]] => [[[[[[.,[.,.]],.],.],.],.],[.,.]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 6
[[[],[]],[],[],[],[[]]] => [[[[[.,[[.,.],.]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 5
[[[[]]],[],[],[],[[]]] => [[[[[.,[.,[.,.]]],.],.],.],[.,.]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => 5
[[[],[],[]],[],[],[[]]] => [[[[.,[[[.,.],.],.]],.],.],[.,.]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 4
[[[],[],[],[],[],[],[]]] => [.,[[[[[[[.,.],.],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 7
[[[],[],[[]],[],[],[]]] => [.,[[[[[[.,.],.],[.,.]],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 6
[[[],[[]],[],[],[],[]]] => [.,[[[[[[.,.],[.,.]],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 6
[[[[]],[],[],[],[],[]]] => [.,[[[[[[.,[.,.]],.],.],.],.],.]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 6
[[[[],[]],[],[],[],[]]] => [.,[[[[[.,[[.,.],.]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 5
[[[[[]]],[],[],[],[]]] => [.,[[[[[.,[.,[.,.]]],.],.],.],.]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 5
[[[[],[],[]],[],[],[]]] => [.,[[[[.,[[[.,.],.],.]],.],.],.]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 4
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Description
The length of a longest cyclic run of ones of a binary word.
Consider the binary word as a cyclic arrangement of ones and zeros. Then this statistic is the length of the longest continuous sequence of ones in this arrangement.
Map
to binary tree: left brother = left child
Description
Return a binary tree of size $n-1$ (where $n$ is the size of $t$, and where $t$ is an ordered tree) by the following recursive rule:
- if $x$ is the left brother of $y$ in $t$, then $x$ becomes the left child of $y$;
- if $x$ is the last child of $y$ in $t$, then $x$ becomes the right child of $y$,
and removing the root of $t$.
Map
to binary word
Description
Return the Dyck word as binary word.
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 $r$.