Processing math: 100%

Identifier
Values
[1,0] => 10 => 1
[1,0,1,0] => 1010 => 2
[1,1,0,0] => 1100 => 2
[1,0,1,0,1,0] => 101010 => 3
[1,0,1,1,0,0] => 101100 => 3
[1,1,0,0,1,0] => 110010 => 3
[1,1,0,1,0,0] => 110100 => 3
[1,1,1,0,0,0] => 111000 => 3
[1,0,1,0,1,0,1,0] => 10101010 => 4
[1,0,1,0,1,1,0,0] => 10101100 => 4
[1,0,1,1,0,0,1,0] => 10110010 => 4
[1,0,1,1,0,1,0,0] => 10110100 => 4
[1,0,1,1,1,0,0,0] => 10111000 => 4
[1,1,0,0,1,0,1,0] => 11001010 => 4
[1,1,0,0,1,1,0,0] => 11001100 => 4
[1,1,0,1,0,0,1,0] => 11010010 => 4
[1,1,0,1,0,1,0,0] => 11010100 => 4
[1,1,0,1,1,0,0,0] => 11011000 => 4
[1,1,1,0,0,0,1,0] => 11100010 => 4
[1,1,1,0,0,1,0,0] => 11100100 => 4
[1,1,1,0,1,0,0,0] => 11101000 => 4
[1,1,1,1,0,0,0,0] => 11110000 => 4
[1,0,1,0,1,0,1,0,1,0] => 1010101010 => 5
[1,0,1,0,1,0,1,1,0,0] => 1010101100 => 5
[1,0,1,0,1,1,0,0,1,0] => 1010110010 => 5
[1,0,1,0,1,1,0,1,0,0] => 1010110100 => 5
[1,0,1,0,1,1,1,0,0,0] => 1010111000 => 5
[1,0,1,1,0,0,1,0,1,0] => 1011001010 => 5
[1,0,1,1,0,0,1,1,0,0] => 1011001100 => 5
[1,0,1,1,0,1,0,0,1,0] => 1011010010 => 5
[1,0,1,1,0,1,0,1,0,0] => 1011010100 => 5
[1,0,1,1,0,1,1,0,0,0] => 1011011000 => 5
[1,0,1,1,1,0,0,0,1,0] => 1011100010 => 5
[1,0,1,1,1,0,0,1,0,0] => 1011100100 => 5
[1,0,1,1,1,0,1,0,0,0] => 1011101000 => 5
[1,0,1,1,1,1,0,0,0,0] => 1011110000 => 5
[1,1,0,0,1,0,1,0,1,0] => 1100101010 => 5
[1,1,0,0,1,0,1,1,0,0] => 1100101100 => 5
[1,1,0,0,1,1,0,0,1,0] => 1100110010 => 5
[1,1,0,0,1,1,0,1,0,0] => 1100110100 => 5
[1,1,0,0,1,1,1,0,0,0] => 1100111000 => 5
[1,1,0,1,0,0,1,0,1,0] => 1101001010 => 5
[1,1,0,1,0,0,1,1,0,0] => 1101001100 => 5
[1,1,0,1,0,1,0,0,1,0] => 1101010010 => 5
[1,1,0,1,0,1,0,1,0,0] => 1101010100 => 5
[1,1,0,1,0,1,1,0,0,0] => 1101011000 => 5
[1,1,0,1,1,0,0,0,1,0] => 1101100010 => 5
[1,1,0,1,1,0,0,1,0,0] => 1101100100 => 5
[1,1,0,1,1,0,1,0,0,0] => 1101101000 => 5
[1,1,0,1,1,1,0,0,0,0] => 1101110000 => 5
[1,1,1,0,0,0,1,0,1,0] => 1110001010 => 5
[1,1,1,0,0,0,1,1,0,0] => 1110001100 => 5
[1,1,1,0,0,1,0,0,1,0] => 1110010010 => 5
[1,1,1,0,0,1,0,1,0,0] => 1110010100 => 5
[1,1,1,0,0,1,1,0,0,0] => 1110011000 => 5
[1,1,1,0,1,0,0,0,1,0] => 1110100010 => 5
[1,1,1,0,1,0,0,1,0,0] => 1110100100 => 5
[1,1,1,0,1,0,1,0,0,0] => 1110101000 => 5
[1,1,1,0,1,1,0,0,0,0] => 1110110000 => 5
[1,1,1,1,0,0,0,0,1,0] => 1111000010 => 5
[1,1,1,1,0,0,0,1,0,0] => 1111000100 => 5
[1,1,1,1,0,0,1,0,0,0] => 1111001000 => 5
[1,1,1,1,0,1,0,0,0,0] => 1111010000 => 5
[1,1,1,1,1,0,0,0,0,0] => 1111100000 => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => 101010101100 => 6
[1,0,1,0,1,0,1,1,0,0,1,0] => 101010110010 => 6
[1,0,1,0,1,0,1,1,0,1,0,0] => 101010110100 => 6
[1,0,1,0,1,0,1,1,1,0,0,0] => 101010111000 => 6
[1,0,1,0,1,1,0,0,1,0,1,0] => 101011001010 => 6
[1,0,1,0,1,1,0,0,1,1,0,0] => 101011001100 => 6
[1,0,1,0,1,1,0,1,0,0,1,0] => 101011010010 => 6
[1,0,1,0,1,1,0,1,0,1,0,0] => 101011010100 => 6
[1,0,1,0,1,1,0,1,1,0,0,0] => 101011011000 => 6
[1,0,1,0,1,1,1,0,0,0,1,0] => 101011100010 => 6
[1,0,1,0,1,1,1,0,0,1,0,0] => 101011100100 => 6
[1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => 6
[1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => 101100101010 => 6
[1,0,1,1,0,0,1,0,1,1,0,0] => 101100101100 => 6
[1,0,1,1,0,0,1,1,0,0,1,0] => 101100110010 => 6
[1,0,1,1,0,0,1,1,0,1,0,0] => 101100110100 => 6
[1,0,1,1,0,0,1,1,1,0,0,0] => 101100111000 => 6
[1,0,1,1,0,1,0,0,1,0,1,0] => 101101001010 => 6
[1,0,1,1,0,1,0,0,1,1,0,0] => 101101001100 => 6
[1,0,1,1,0,1,0,1,0,0,1,0] => 101101010010 => 6
[1,0,1,1,0,1,0,1,0,1,0,0] => 101101010100 => 6
[1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 6
[1,0,1,1,0,1,1,0,0,0,1,0] => 101101100010 => 6
[1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => 6
[1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 6
[1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 6
[1,0,1,1,1,0,0,0,1,0,1,0] => 101110001010 => 6
[1,0,1,1,1,0,0,0,1,1,0,0] => 101110001100 => 6
[1,0,1,1,1,0,0,1,0,0,1,0] => 101110010010 => 6
[1,0,1,1,1,0,0,1,0,1,0,0] => 101110010100 => 6
[1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 6
[1,0,1,1,1,0,1,0,0,0,1,0] => 101110100010 => 6
[1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => 6
[1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 6
[1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 6
>>> Load all 250 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 6
[1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 6
[1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 6
[1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 6
[1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 6
[1,1,0,0,1,0,1,0,1,0,1,0] => 110010101010 => 6
[1,1,0,0,1,0,1,0,1,1,0,0] => 110010101100 => 6
[1,1,0,0,1,0,1,1,0,0,1,0] => 110010110010 => 6
[1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => 6
[1,1,0,0,1,0,1,1,1,0,0,0] => 110010111000 => 6
[1,1,0,0,1,1,0,0,1,0,1,0] => 110011001010 => 6
[1,1,0,0,1,1,0,0,1,1,0,0] => 110011001100 => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => 110011010010 => 6
[1,1,0,0,1,1,0,1,0,1,0,0] => 110011010100 => 6
[1,1,0,0,1,1,0,1,1,0,0,0] => 110011011000 => 6
[1,1,0,0,1,1,1,0,0,0,1,0] => 110011100010 => 6
[1,1,0,0,1,1,1,0,0,1,0,0] => 110011100100 => 6
[1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => 6
[1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 6
[1,1,0,1,0,0,1,0,1,0,1,0] => 110100101010 => 6
[1,1,0,1,0,0,1,0,1,1,0,0] => 110100101100 => 6
[1,1,0,1,0,0,1,1,0,0,1,0] => 110100110010 => 6
[1,1,0,1,0,0,1,1,0,1,0,0] => 110100110100 => 6
[1,1,0,1,0,0,1,1,1,0,0,0] => 110100111000 => 6
[1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => 6
[1,1,0,1,0,1,0,0,1,1,0,0] => 110101001100 => 6
[1,1,0,1,0,1,0,1,0,0,1,0] => 110101010010 => 6
[1,1,0,1,0,1,0,1,0,1,0,0] => 110101010100 => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => 110101011000 => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => 110101100010 => 6
[1,1,0,1,0,1,1,0,0,1,0,0] => 110101100100 => 6
[1,1,0,1,0,1,1,0,1,0,0,0] => 110101101000 => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => 110101110000 => 6
[1,1,0,1,1,0,0,0,1,0,1,0] => 110110001010 => 6
[1,1,0,1,1,0,0,0,1,1,0,0] => 110110001100 => 6
[1,1,0,1,1,0,0,1,0,0,1,0] => 110110010010 => 6
[1,1,0,1,1,0,0,1,0,1,0,0] => 110110010100 => 6
[1,1,0,1,1,0,0,1,1,0,0,0] => 110110011000 => 6
[1,1,0,1,1,0,1,0,0,0,1,0] => 110110100010 => 6
[1,1,0,1,1,0,1,0,0,1,0,0] => 110110100100 => 6
[1,1,0,1,1,0,1,0,1,0,0,0] => 110110101000 => 6
[1,1,0,1,1,0,1,1,0,0,0,0] => 110110110000 => 6
[1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 6
[1,1,0,1,1,1,0,0,0,1,0,0] => 110111000100 => 6
[1,1,0,1,1,1,0,0,1,0,0,0] => 110111001000 => 6
[1,1,0,1,1,1,0,1,0,0,0,0] => 110111010000 => 6
[1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 6
[1,1,1,0,0,0,1,0,1,0,1,0] => 111000101010 => 6
[1,1,1,0,0,0,1,0,1,1,0,0] => 111000101100 => 6
[1,1,1,0,0,0,1,1,0,0,1,0] => 111000110010 => 6
[1,1,1,0,0,0,1,1,0,1,0,0] => 111000110100 => 6
[1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 6
[1,1,1,0,0,1,0,0,1,0,1,0] => 111001001010 => 6
[1,1,1,0,0,1,0,0,1,1,0,0] => 111001001100 => 6
[1,1,1,0,0,1,0,1,0,0,1,0] => 111001010010 => 6
[1,1,1,0,0,1,0,1,0,1,0,0] => 111001010100 => 6
[1,1,1,0,0,1,0,1,1,0,0,0] => 111001011000 => 6
[1,1,1,0,0,1,1,0,0,0,1,0] => 111001100010 => 6
[1,1,1,0,0,1,1,0,0,1,0,0] => 111001100100 => 6
[1,1,1,0,0,1,1,0,1,0,0,0] => 111001101000 => 6
[1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 6
[1,1,1,0,1,0,0,0,1,0,1,0] => 111010001010 => 6
[1,1,1,0,1,0,0,0,1,1,0,0] => 111010001100 => 6
[1,1,1,0,1,0,0,1,0,0,1,0] => 111010010010 => 6
[1,1,1,0,1,0,0,1,0,1,0,0] => 111010010100 => 6
[1,1,1,0,1,0,0,1,1,0,0,0] => 111010011000 => 6
[1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => 6
[1,1,1,0,1,0,1,0,0,1,0,0] => 111010100100 => 6
[1,1,1,0,1,0,1,0,1,0,0,0] => 111010101000 => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => 111010110000 => 6
[1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 6
[1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => 6
[1,1,1,0,1,1,0,0,1,0,0,0] => 111011001000 => 6
[1,1,1,0,1,1,0,1,0,0,0,0] => 111011010000 => 6
[1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 6
[1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 6
[1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 6
[1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 6
[1,1,1,1,0,0,0,1,0,1,0,0] => 111100010100 => 6
[1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 6
[1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 6
[1,1,1,1,0,0,1,0,0,1,0,0] => 111100100100 => 6
[1,1,1,1,0,0,1,0,1,0,0,0] => 111100101000 => 6
[1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 6
[1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 6
[1,1,1,1,0,1,0,0,0,1,0,0] => 111101000100 => 6
[1,1,1,1,0,1,0,0,1,0,0,0] => 111101001000 => 6
[1,1,1,1,0,1,0,1,0,0,0,0] => 111101010000 => 6
[1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 6
[1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 6
[1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 6
[1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 6
[1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 6
[1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 6
[1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 7
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => 7
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 7
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 7
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 10111101001000 => 7
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 7
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 7
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11101101000010 => 7
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 7
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 7
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11110100100010 => 7
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11110101000010 => 7
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 7
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 7
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 7
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 7
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 7
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 7
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 7
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 8
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 8
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 8
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 8
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 8
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 8
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 8
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => 8
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 8
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 8
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 8
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 8
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => 9
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 9
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 11111111100000000010 => 10
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 111111101000000010 => 9
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 101111111010000000 => 9
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 10
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1111111111000000000010 => 11
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 11111111010000000010 => 10
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 111111100100000010 => 9
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 111111011000000010 => 9
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 101111111001000000 => 9
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 101111110110000000 => 9
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 10111111110100000000 => 10
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1011111111110000000000 => 11
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Description
The semilength of the longest Dyck word in the Catalan factorisation of a binary word.
Every binary word can be written in a unique way as (D0)ℓD(1D)m, where D is the set of Dyck words. This is the Catalan factorisation, see [1, sec.9.1.2].
This statistic records the semilength of the longest Dyck word in this factorisation.
Map
to binary word
Description
Return the Dyck word as binary word.