Identifier
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00268: Binary words —zeros to flag zeros⟶ Binary words
Images
[1,0] => 10 => 01
[1,0,1,0] => 1010 => 1001
[1,1,0,0] => 1100 => 1011
[1,0,1,0,1,0] => 101010 => 011001
[1,0,1,1,0,0] => 101100 => 010001
[1,1,0,0,1,0] => 110010 => 011011
[1,1,0,1,0,0] => 110100 => 010011
[1,1,1,0,0,0] => 111000 => 010111
[1,0,1,0,1,0,1,0] => 10101010 => 10011001
[1,0,1,0,1,1,0,0] => 10101100 => 10111001
[1,0,1,1,0,0,1,0] => 10110010 => 10010001
[1,0,1,1,0,1,0,0] => 10110100 => 10110001
[1,0,1,1,1,0,0,0] => 10111000 => 10100001
[1,1,0,0,1,0,1,0] => 11001010 => 10011011
[1,1,0,0,1,1,0,0] => 11001100 => 10111011
[1,1,0,1,0,0,1,0] => 11010010 => 10010011
[1,1,0,1,0,1,0,0] => 11010100 => 10110011
[1,1,0,1,1,0,0,0] => 11011000 => 10100011
[1,1,1,0,0,0,1,0] => 11100010 => 10010111
[1,1,1,0,0,1,0,0] => 11100100 => 10110111
[1,1,1,0,1,0,0,0] => 11101000 => 10100111
[1,1,1,1,0,0,0,0] => 11110000 => 10101111
[1,0,1,0,1,0,1,0,1,0] => 1010101010 => 0110011001
[1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0100011001
[1,0,1,0,1,1,0,0,1,0] => 1010110010 => 0110111001
[1,0,1,0,1,1,0,1,0,0] => 1010110100 => 0100111001
[1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0101111001
[1,0,1,1,0,0,1,0,1,0] => 1011001010 => 0110010001
[1,0,1,1,0,0,1,1,0,0] => 1011001100 => 0100010001
[1,0,1,1,0,1,0,0,1,0] => 1011010010 => 0110110001
[1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0100110001
[1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0101110001
[1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0110100001
[1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0100100001
[1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0101100001
[1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0101000001
[1,1,0,0,1,0,1,0,1,0] => 1100101010 => 0110011011
[1,1,0,0,1,0,1,1,0,0] => 1100101100 => 0100011011
[1,1,0,0,1,1,0,0,1,0] => 1100110010 => 0110111011
[1,1,0,0,1,1,0,1,0,0] => 1100110100 => 0100111011
[1,1,0,0,1,1,1,0,0,0] => 1100111000 => 0101111011
[1,1,0,1,0,0,1,0,1,0] => 1101001010 => 0110010011
[1,1,0,1,0,0,1,1,0,0] => 1101001100 => 0100010011
[1,1,0,1,0,1,0,0,1,0] => 1101010010 => 0110110011
[1,1,0,1,0,1,0,1,0,0] => 1101010100 => 0100110011
[1,1,0,1,0,1,1,0,0,0] => 1101011000 => 0101110011
[1,1,0,1,1,0,0,0,1,0] => 1101100010 => 0110100011
[1,1,0,1,1,0,0,1,0,0] => 1101100100 => 0100100011
[1,1,0,1,1,0,1,0,0,0] => 1101101000 => 0101100011
[1,1,0,1,1,1,0,0,0,0] => 1101110000 => 0101000011
[1,1,1,0,0,0,1,0,1,0] => 1110001010 => 0110010111
[1,1,1,0,0,0,1,1,0,0] => 1110001100 => 0100010111
[1,1,1,0,0,1,0,0,1,0] => 1110010010 => 0110110111
[1,1,1,0,0,1,0,1,0,0] => 1110010100 => 0100110111
[1,1,1,0,0,1,1,0,0,0] => 1110011000 => 0101110111
[1,1,1,0,1,0,0,0,1,0] => 1110100010 => 0110100111
[1,1,1,0,1,0,0,1,0,0] => 1110100100 => 0100100111
[1,1,1,0,1,0,1,0,0,0] => 1110101000 => 0101100111
[1,1,1,0,1,1,0,0,0,0] => 1110110000 => 0101000111
[1,1,1,1,0,0,0,0,1,0] => 1111000010 => 0110101111
[1,1,1,1,0,0,0,1,0,0] => 1111000100 => 0100101111
[1,1,1,1,0,0,1,0,0,0] => 1111001000 => 0101101111
[1,1,1,1,0,1,0,0,0,0] => 1111010000 => 0101001111
[1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0101011111
[1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => 100110011001
[1,0,1,0,1,0,1,0,1,1,0,0] => 101010101100 => 101110011001
[1,0,1,0,1,0,1,1,0,0,1,0] => 101010110010 => 100100011001
[1,0,1,0,1,0,1,1,0,1,0,0] => 101010110100 => 101100011001
[1,0,1,0,1,0,1,1,1,0,0,0] => 101010111000 => 101000011001
[1,0,1,0,1,1,0,0,1,0,1,0] => 101011001010 => 100110111001
[1,0,1,0,1,1,0,0,1,1,0,0] => 101011001100 => 101110111001
[1,0,1,0,1,1,0,1,0,0,1,0] => 101011010010 => 100100111001
[1,0,1,0,1,1,0,1,0,1,0,0] => 101011010100 => 101100111001
[1,0,1,0,1,1,0,1,1,0,0,0] => 101011011000 => 101000111001
[1,0,1,0,1,1,1,0,0,0,1,0] => 101011100010 => 100101111001
[1,0,1,0,1,1,1,0,0,1,0,0] => 101011100100 => 101101111001
[1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => 101001111001
[1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 101011111001
[1,0,1,1,0,0,1,0,1,0,1,0] => 101100101010 => 100110010001
[1,0,1,1,0,0,1,0,1,1,0,0] => 101100101100 => 101110010001
[1,0,1,1,0,0,1,1,0,0,1,0] => 101100110010 => 100100010001
[1,0,1,1,0,0,1,1,0,1,0,0] => 101100110100 => 101100010001
[1,0,1,1,0,0,1,1,1,0,0,0] => 101100111000 => 101000010001
[1,0,1,1,0,1,0,0,1,0,1,0] => 101101001010 => 100110110001
[1,0,1,1,0,1,0,0,1,1,0,0] => 101101001100 => 101110110001
[1,0,1,1,0,1,0,1,0,0,1,0] => 101101010010 => 100100110001
[1,0,1,1,0,1,0,1,0,1,0,0] => 101101010100 => 101100110001
[1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 101000110001
[1,0,1,1,0,1,1,0,0,0,1,0] => 101101100010 => 100101110001
[1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => 101101110001
[1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 101001110001
[1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 101011110001
[1,0,1,1,1,0,0,0,1,0,1,0] => 101110001010 => 100110100001
[1,0,1,1,1,0,0,0,1,1,0,0] => 101110001100 => 101110100001
[1,0,1,1,1,0,0,1,0,0,1,0] => 101110010010 => 100100100001
[1,0,1,1,1,0,0,1,0,1,0,0] => 101110010100 => 101100100001
[1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 101000100001
[1,0,1,1,1,0,1,0,0,0,1,0] => 101110100010 => 100101100001
[1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => 101101100001
[1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 101001100001
[1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 101011100001
>>> Load all 455 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 100101000001
[1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 101101000001
[1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 101001000001
[1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 101011000001
[1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 101010000001
[1,1,0,0,1,0,1,0,1,0,1,0] => 110010101010 => 100110011011
[1,1,0,0,1,0,1,0,1,1,0,0] => 110010101100 => 101110011011
[1,1,0,0,1,0,1,1,0,0,1,0] => 110010110010 => 100100011011
[1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => 101100011011
[1,1,0,0,1,0,1,1,1,0,0,0] => 110010111000 => 101000011011
[1,1,0,0,1,1,0,0,1,0,1,0] => 110011001010 => 100110111011
[1,1,0,0,1,1,0,0,1,1,0,0] => 110011001100 => 101110111011
[1,1,0,0,1,1,0,1,0,0,1,0] => 110011010010 => 100100111011
[1,1,0,0,1,1,0,1,0,1,0,0] => 110011010100 => 101100111011
[1,1,0,0,1,1,0,1,1,0,0,0] => 110011011000 => 101000111011
[1,1,0,0,1,1,1,0,0,0,1,0] => 110011100010 => 100101111011
[1,1,0,0,1,1,1,0,0,1,0,0] => 110011100100 => 101101111011
[1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => 101001111011
[1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 101011111011
[1,1,0,1,0,0,1,0,1,0,1,0] => 110100101010 => 100110010011
[1,1,0,1,0,0,1,0,1,1,0,0] => 110100101100 => 101110010011
[1,1,0,1,0,0,1,1,0,0,1,0] => 110100110010 => 100100010011
[1,1,0,1,0,0,1,1,0,1,0,0] => 110100110100 => 101100010011
[1,1,0,1,0,0,1,1,1,0,0,0] => 110100111000 => 101000010011
[1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => 100110110011
[1,1,0,1,0,1,0,0,1,1,0,0] => 110101001100 => 101110110011
[1,1,0,1,0,1,0,1,0,0,1,0] => 110101010010 => 100100110011
[1,1,0,1,0,1,0,1,0,1,0,0] => 110101010100 => 101100110011
[1,1,0,1,0,1,0,1,1,0,0,0] => 110101011000 => 101000110011
[1,1,0,1,0,1,1,0,0,0,1,0] => 110101100010 => 100101110011
[1,1,0,1,0,1,1,0,0,1,0,0] => 110101100100 => 101101110011
[1,1,0,1,0,1,1,0,1,0,0,0] => 110101101000 => 101001110011
[1,1,0,1,0,1,1,1,0,0,0,0] => 110101110000 => 101011110011
[1,1,0,1,1,0,0,0,1,0,1,0] => 110110001010 => 100110100011
[1,1,0,1,1,0,0,0,1,1,0,0] => 110110001100 => 101110100011
[1,1,0,1,1,0,0,1,0,0,1,0] => 110110010010 => 100100100011
[1,1,0,1,1,0,0,1,0,1,0,0] => 110110010100 => 101100100011
[1,1,0,1,1,0,0,1,1,0,0,0] => 110110011000 => 101000100011
[1,1,0,1,1,0,1,0,0,0,1,0] => 110110100010 => 100101100011
[1,1,0,1,1,0,1,0,0,1,0,0] => 110110100100 => 101101100011
[1,1,0,1,1,0,1,0,1,0,0,0] => 110110101000 => 101001100011
[1,1,0,1,1,0,1,1,0,0,0,0] => 110110110000 => 101011100011
[1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 100101000011
[1,1,0,1,1,1,0,0,0,1,0,0] => 110111000100 => 101101000011
[1,1,0,1,1,1,0,0,1,0,0,0] => 110111001000 => 101001000011
[1,1,0,1,1,1,0,1,0,0,0,0] => 110111010000 => 101011000011
[1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 101010000011
[1,1,1,0,0,0,1,0,1,0,1,0] => 111000101010 => 100110010111
[1,1,1,0,0,0,1,0,1,1,0,0] => 111000101100 => 101110010111
[1,1,1,0,0,0,1,1,0,0,1,0] => 111000110010 => 100100010111
[1,1,1,0,0,0,1,1,0,1,0,0] => 111000110100 => 101100010111
[1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 101000010111
[1,1,1,0,0,1,0,0,1,0,1,0] => 111001001010 => 100110110111
[1,1,1,0,0,1,0,0,1,1,0,0] => 111001001100 => 101110110111
[1,1,1,0,0,1,0,1,0,0,1,0] => 111001010010 => 100100110111
[1,1,1,0,0,1,0,1,0,1,0,0] => 111001010100 => 101100110111
[1,1,1,0,0,1,0,1,1,0,0,0] => 111001011000 => 101000110111
[1,1,1,0,0,1,1,0,0,0,1,0] => 111001100010 => 100101110111
[1,1,1,0,0,1,1,0,0,1,0,0] => 111001100100 => 101101110111
[1,1,1,0,0,1,1,0,1,0,0,0] => 111001101000 => 101001110111
[1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 101011110111
[1,1,1,0,1,0,0,0,1,0,1,0] => 111010001010 => 100110100111
[1,1,1,0,1,0,0,0,1,1,0,0] => 111010001100 => 101110100111
[1,1,1,0,1,0,0,1,0,0,1,0] => 111010010010 => 100100100111
[1,1,1,0,1,0,0,1,0,1,0,0] => 111010010100 => 101100100111
[1,1,1,0,1,0,0,1,1,0,0,0] => 111010011000 => 101000100111
[1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => 100101100111
[1,1,1,0,1,0,1,0,0,1,0,0] => 111010100100 => 101101100111
[1,1,1,0,1,0,1,0,1,0,0,0] => 111010101000 => 101001100111
[1,1,1,0,1,0,1,1,0,0,0,0] => 111010110000 => 101011100111
[1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 100101000111
[1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => 101101000111
[1,1,1,0,1,1,0,0,1,0,0,0] => 111011001000 => 101001000111
[1,1,1,0,1,1,0,1,0,0,0,0] => 111011010000 => 101011000111
[1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 101010000111
[1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 100110101111
[1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 101110101111
[1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 100100101111
[1,1,1,1,0,0,0,1,0,1,0,0] => 111100010100 => 101100101111
[1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 101000101111
[1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 100101101111
[1,1,1,1,0,0,1,0,0,1,0,0] => 111100100100 => 101101101111
[1,1,1,1,0,0,1,0,1,0,0,0] => 111100101000 => 101001101111
[1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 101011101111
[1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 100101001111
[1,1,1,1,0,1,0,0,0,1,0,0] => 111101000100 => 101101001111
[1,1,1,1,0,1,0,0,1,0,0,0] => 111101001000 => 101001001111
[1,1,1,1,0,1,0,1,0,0,0,0] => 111101010000 => 101011001111
[1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 101010001111
[1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 100101011111
[1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 101101011111
[1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 101001011111
[1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 101011011111
[1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 101010011111
[1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 101010111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10101010101010 => 01100110011001
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 10101010101100 => 01000110011001
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 10101010110100 => 01001110011001
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 10101010111000 => 01011110011001
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 10101011010100 => 01001100011001
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 10101011100100 => 01001000011001
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 10101011101000 => 01011000011001
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10101011110000 => 01010000011001
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 10101101010100 => 01001100111001
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 10101110010100 => 01001101111001
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 10101110100100 => 01001001111001
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 10101110101000 => 01011001111001
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 10101110110000 => 01010001111001
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 10101111000100 => 01001011111001
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 10101111010000 => 01010011111001
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 10110101010100 => 01001100110001
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10110111100000 => 01010111110001
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 10111001010100 => 01001100100001
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 10111010010100 => 01001101100001
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 10111010100100 => 01001001100001
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 10111011000100 => 01001011100001
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10111011010000 => 01010011100001
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10111011100000 => 01010111100001
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 10111100010100 => 01001101000001
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 10111100110000 => 01010001000001
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 10111101000100 => 01001011000001
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 10111101001000 => 01011011000001
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 10111101010000 => 01010011000001
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 10111101100000 => 01010111000001
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10111110000100 => 01001010000001
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10111110001000 => 01011010000001
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10111110010000 => 01010010000001
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10111110100000 => 01010110000001
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10111111000000 => 01010100000001
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11001111100000 => 01010111111011
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 11010101010100 => 01001100110011
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 11010101011000 => 01011100110011
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 11010101100100 => 01001000110011
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 11010101101000 => 01011000110011
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 11010101110000 => 01010000110011
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 11010110010100 => 01001101110011
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 11010110011000 => 01011101110011
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 11010110100100 => 01001001110011
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 11010110101000 => 01011001110011
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 11010110110000 => 01010001110011
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 11010111000100 => 01001011110011
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 11010111001000 => 01011011110011
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 11010111010000 => 01010011110011
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 11010111100000 => 01010111110011
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 11011001010100 => 01001100100011
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 11011001011000 => 01011100100011
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 11011001100100 => 01001000100011
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 11011001101000 => 01011000100011
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 11011001110000 => 01010000100011
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 11011010010100 => 01001101100011
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 11011010011000 => 01011101100011
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 11011010100100 => 01001001100011
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 11011010101000 => 01011001100011
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 11011010110000 => 01010001100011
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 11011011000100 => 01001011100011
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 11011011001000 => 01011011100011
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 11011011010000 => 01010011100011
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 11011011100000 => 01010111100011
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 11011100010100 => 01001101000011
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 11011100011000 => 01011101000011
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 11011100100100 => 01001001000011
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 11011100101000 => 01011001000011
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 11011100110000 => 01010001000011
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 11011101000100 => 01001011000011
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 11011101001000 => 01011011000011
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 11011101010000 => 01010011000011
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 11011101100000 => 01010111000011
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 11011110000010 => 01101010000011
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 11011110000100 => 01001010000011
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 11011110001000 => 01011010000011
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 11011110010000 => 01010010000011
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 11011110100000 => 01010110000011
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 11011111000000 => 01010100000011
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 11100101010100 => 01001100110111
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 11100101011000 => 01011100110111
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 11100101100100 => 01001000110111
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 11100101101000 => 01011000110111
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 11100101110000 => 01010000110111
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 11100110010100 => 01001101110111
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 11100110011000 => 01011101110111
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 11100110100100 => 01001001110111
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 11100110101000 => 01011001110111
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 11100110110000 => 01010001110111
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 11100111000100 => 01001011110111
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 11100111001000 => 01011011110111
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 11100111010000 => 01010011110111
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 11100111100000 => 01010111110111
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 11101001010100 => 01001100100111
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 11101001011000 => 01011100100111
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 11101001100100 => 01001000100111
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 11101001101000 => 01011000100111
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 11101001110000 => 01010000100111
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 11101010010100 => 01001101100111
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 11101010011000 => 01011101100111
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 11101010100100 => 01001001100111
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 11101010101000 => 01011001100111
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 11101010110000 => 01010001100111
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 11101011000100 => 01001011100111
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 11101011001000 => 01011011100111
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 11101011010000 => 01010011100111
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 11101011100000 => 01010111100111
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 11101100010100 => 01001101000111
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 11101100011000 => 01011101000111
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 11101100100100 => 01001001000111
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 11101100101000 => 01011001000111
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 11101100110000 => 01010001000111
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 11101101000010 => 01101011000111
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 11101101000100 => 01001011000111
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 11101101001000 => 01011011000111
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 11101101010000 => 01010011000111
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 11101101100000 => 01010111000111
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11101110000010 => 01101010000111
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11101110000100 => 01001010000111
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 11101110001000 => 01011010000111
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 11101110010000 => 01010010000111
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 11101110100000 => 01010110000111
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 11101111000000 => 01010100000111
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 11110001010100 => 01001100101111
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 11110001011000 => 01011100101111
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 11110001100100 => 01001000101111
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 11110001101000 => 01011000101111
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 11110001110000 => 01010000101111
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 11110010010100 => 01001101101111
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 11110010011000 => 01011101101111
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 11110010100100 => 01001001101111
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 11110010101000 => 01011001101111
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 11110010110000 => 01010001101111
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 11110011000010 => 01101011101111
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 11110011000100 => 01001011101111
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 11110011001000 => 01011011101111
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 11110011010000 => 01010011101111
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 11110011100000 => 01010111101111
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 11110100010100 => 01001101001111
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 11110100011000 => 01011101001111
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 11110100100010 => 01101001001111
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 11110100100100 => 01001001001111
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 11110100101000 => 01011001001111
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 11110100110000 => 01010001001111
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 11110101000010 => 01101011001111
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 11110101000100 => 01001011001111
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 11110101001000 => 01011011001111
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 11110101010000 => 01010011001111
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 11110101100000 => 01010111001111
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 11110110000010 => 01101010001111
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 11110110000100 => 01001010001111
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 11110110001000 => 01011010001111
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 11110110010000 => 01010010001111
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 11110110100000 => 01010110001111
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 11110111000000 => 01010100001111
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11111000001100 => 01000101011111
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 11111000010010 => 01101101011111
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 11111000010100 => 01001101011111
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 11111000011000 => 01011101011111
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 11111000100010 => 01101001011111
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 11111000100100 => 01001001011111
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 11111000101000 => 01011001011111
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 11111000110000 => 01010001011111
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 11111001000010 => 01101011011111
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 11111001000100 => 01001011011111
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 11111001001000 => 01011011011111
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 11111001010000 => 01010011011111
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 11111001100000 => 01010111011111
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11111010000010 => 01101010011111
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 11111010000100 => 01001010011111
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 11111010001000 => 01011010011111
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 11111010010000 => 01010010011111
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 11111010100000 => 01010110011111
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 11111011000000 => 01010100011111
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 11111100000010 => 01101010111111
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 11111100000100 => 01001010111111
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 11111100001000 => 01011010111111
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 11111100010000 => 01010010111111
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 11111100100000 => 01010110111111
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 11111101000000 => 01010100111111
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 11111110000000 => 01010101111111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1010101010101010 => 1001100110011001
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1010101010101100 => 1011100110011001
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1010101010110100 => 1011000110011001
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1010101010111000 => 1010000110011001
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1010101011010100 => 1011001110011001
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 1010101011100100 => 1011011110011001
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1010101011101000 => 1010011110011001
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 1010101011110000 => 1010111110011001
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1010101101010100 => 1011001100011001
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 1010101110010100 => 1011001000011001
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1010101110100100 => 1011011000011001
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 1010101111000100 => 1011010000011001
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1010110101010100 => 1011001100111001
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 1010111001010100 => 1011001101111001
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1010111010010100 => 1011001001111001
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 1010111100010100 => 1011001011111001
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1011010101010100 => 1011001100110001
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 1011100101010100 => 1011001100100001
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1011101001010100 => 1011001101100001
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 1011110001010100 => 1011001101000001
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1011110111000000 => 1010101111000001
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1011111010100000 => 1010100110000001
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1011111011000000 => 1010101110000001
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1011111100010000 => 1010110100000001
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1011111100100000 => 1010100100000001
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1011111101000000 => 1010101100000001
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1011111110000000 => 1010101000000001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1101010101010100 => 1011001100110011
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 1110010101010100 => 1011001100110111
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => 1110100101010100 => 1011001100100111
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => 1111000101010100 => 1011001100101111
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => 1111011100000010 => 1001010100001111
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => 1111101010000010 => 1001010110011111
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => 1111101100000010 => 1001010100011111
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => 1111110001000010 => 1001010010111111
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => 1111110010000010 => 1001010110111111
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => 1111110100000010 => 1001010100111111
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 1111111000000010 => 1001010101111111
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 111111110000000010 => 011010101011111111
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 101111111100000000 => 010101010000000001
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 11111111100000000010 => 10010101010111111111
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => 111111101000000010 => 011010101001111111
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 101111111010000000 => 010101011000000001
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 10111111111000000000 => 10101010100000000001
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => 1111111111000000000010 => 0110101010101111111111
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => 11111111010000000010 => 10010101010011111111
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => 111111100100000010 => 011010101101111111
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => 111111011000000010 => 011010101000111111
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => 101111111001000000 => 010101001000000001
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 101111110110000000 => 010101011100000001
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => 10111111110100000000 => 10101010110000000001
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 1011111111110000000000 => 0101010101000000000001
[] => =>
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 110101010101010100 => 010011001100110011
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 111001010101010100 => 010011001100110111
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010101010 => 011001100110011001
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 101010101010101100 => 010001100110011001
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 101010101010110100 => 010011100110011001
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 101010101011010100 => 010011000110011001
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 101010101101010100 => 010011001110011001
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 101010110101010100 => 010011001100011001
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 101011010101010100 => 010011001100111001
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 101101010101010100 => 010011001100110001
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10101010101010101010 => 10011001100110011001
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 10101010101010101100 => 10111001100110011001
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 101010101010111000 => 010111100110011001
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 10101010101010110100 => 10110001100110011001
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 101010101011100100 => 010010000110011001
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 10101010101011010100 => 10110011100110011001
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 101010101110010100 => 010011011110011001
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 10101010101101010100 => 10110011000110011001
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 101010111001010100 => 010011001000011001
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 10101010110101010100 => 10110011001110011001
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 101011100101010100 => 010011001101111001
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10101011010101010100 => 10110011001100011001
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => 101110010101010100 => 010011001100100001
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10101101010101010100 => 10110011001100111001
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 10110101010101010100 => 10110011001100110001
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => 11010101010101010100 => 10110011001100110011
Map
to binary word
Description
Return the Dyck word as binary word.
Map
zeros to flag zeros
Description
Return a binary word of the same length, such that the number of occurrences of $10$ in the word obtained by prepending the reverse of the complement equals the number of $0$s in the original word.
For example, the image of the word $w=1\dots1$ is $1\dots1$, because $w$ has no zeros, and $1\dots1$ is the only word such that prepending the reverse of its complement has no occurrence of the factor $10$.
On the other hand, $0\dots0$ must be mapped to $10\dots10$ if the length is even, and $010\dots10$ if it is odd.