Identifier
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Images
[1,0] => 10 => 01 => [2,1]
[1,0,1,0] => 1010 => 0101 => [2,2,1]
[1,1,0,0] => 1100 => 1001 => [1,3,1]
[1,0,1,0,1,0] => 101010 => 010101 => [2,2,2,1]
[1,0,1,1,0,0] => 101100 => 011001 => [2,1,3,1]
[1,1,0,0,1,0] => 110010 => 100101 => [1,3,2,1]
[1,1,0,1,0,0] => 110100 => 101001 => [1,2,3,1]
[1,1,1,0,0,0] => 111000 => 110001 => [1,1,4,1]
[1,0,1,0,1,0,1,0] => 10101010 => 01010101 => [2,2,2,2,1]
[1,0,1,0,1,1,0,0] => 10101100 => 01011001 => [2,2,1,3,1]
[1,0,1,1,0,0,1,0] => 10110010 => 01100101 => [2,1,3,2,1]
[1,0,1,1,0,1,0,0] => 10110100 => 01101001 => [2,1,2,3,1]
[1,0,1,1,1,0,0,0] => 10111000 => 01110001 => [2,1,1,4,1]
[1,1,0,0,1,0,1,0] => 11001010 => 10010101 => [1,3,2,2,1]
[1,1,0,0,1,1,0,0] => 11001100 => 10011001 => [1,3,1,3,1]
[1,1,0,1,0,0,1,0] => 11010010 => 10100101 => [1,2,3,2,1]
[1,1,0,1,0,1,0,0] => 11010100 => 10101001 => [1,2,2,3,1]
[1,1,0,1,1,0,0,0] => 11011000 => 10110001 => [1,2,1,4,1]
[1,1,1,0,0,0,1,0] => 11100010 => 11000101 => [1,1,4,2,1]
[1,1,1,0,0,1,0,0] => 11100100 => 11001001 => [1,1,3,3,1]
[1,1,1,0,1,0,0,0] => 11101000 => 11010001 => [1,1,2,4,1]
[1,1,1,1,0,0,0,0] => 11110000 => 11100001 => [1,1,1,5,1]
[1,0,1,0,1,0,1,0,1,0] => 1010101010 => 0101010101 => [2,2,2,2,2,1]
[1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0101011001 => [2,2,2,1,3,1]
[1,0,1,0,1,1,0,0,1,0] => 1010110010 => 0101100101 => [2,2,1,3,2,1]
[1,0,1,0,1,1,0,1,0,0] => 1010110100 => 0101101001 => [2,2,1,2,3,1]
[1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0101110001 => [2,2,1,1,4,1]
[1,0,1,1,0,0,1,0,1,0] => 1011001010 => 0110010101 => [2,1,3,2,2,1]
[1,0,1,1,0,0,1,1,0,0] => 1011001100 => 0110011001 => [2,1,3,1,3,1]
[1,0,1,1,0,1,0,0,1,0] => 1011010010 => 0110100101 => [2,1,2,3,2,1]
[1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0110101001 => [2,1,2,2,3,1]
[1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0110110001 => [2,1,2,1,4,1]
[1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0111000101 => [2,1,1,4,2,1]
[1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0111001001 => [2,1,1,3,3,1]
[1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0111010001 => [2,1,1,2,4,1]
[1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0111100001 => [2,1,1,1,5,1]
[1,1,0,0,1,0,1,0,1,0] => 1100101010 => 1001010101 => [1,3,2,2,2,1]
[1,1,0,0,1,0,1,1,0,0] => 1100101100 => 1001011001 => [1,3,2,1,3,1]
[1,1,0,0,1,1,0,0,1,0] => 1100110010 => 1001100101 => [1,3,1,3,2,1]
[1,1,0,0,1,1,0,1,0,0] => 1100110100 => 1001101001 => [1,3,1,2,3,1]
[1,1,0,0,1,1,1,0,0,0] => 1100111000 => 1001110001 => [1,3,1,1,4,1]
[1,1,0,1,0,0,1,0,1,0] => 1101001010 => 1010010101 => [1,2,3,2,2,1]
[1,1,0,1,0,0,1,1,0,0] => 1101001100 => 1010011001 => [1,2,3,1,3,1]
[1,1,0,1,0,1,0,0,1,0] => 1101010010 => 1010100101 => [1,2,2,3,2,1]
[1,1,0,1,0,1,0,1,0,0] => 1101010100 => 1010101001 => [1,2,2,2,3,1]
[1,1,0,1,0,1,1,0,0,0] => 1101011000 => 1010110001 => [1,2,2,1,4,1]
[1,1,0,1,1,0,0,0,1,0] => 1101100010 => 1011000101 => [1,2,1,4,2,1]
[1,1,0,1,1,0,0,1,0,0] => 1101100100 => 1011001001 => [1,2,1,3,3,1]
[1,1,0,1,1,0,1,0,0,0] => 1101101000 => 1011010001 => [1,2,1,2,4,1]
[1,1,0,1,1,1,0,0,0,0] => 1101110000 => 1011100001 => [1,2,1,1,5,1]
[1,1,1,0,0,0,1,0,1,0] => 1110001010 => 1100010101 => [1,1,4,2,2,1]
[1,1,1,0,0,0,1,1,0,0] => 1110001100 => 1100011001 => [1,1,4,1,3,1]
[1,1,1,0,0,1,0,0,1,0] => 1110010010 => 1100100101 => [1,1,3,3,2,1]
[1,1,1,0,0,1,0,1,0,0] => 1110010100 => 1100101001 => [1,1,3,2,3,1]
[1,1,1,0,0,1,1,0,0,0] => 1110011000 => 1100110001 => [1,1,3,1,4,1]
[1,1,1,0,1,0,0,0,1,0] => 1110100010 => 1101000101 => [1,1,2,4,2,1]
[1,1,1,0,1,0,0,1,0,0] => 1110100100 => 1101001001 => [1,1,2,3,3,1]
[1,1,1,0,1,0,1,0,0,0] => 1110101000 => 1101010001 => [1,1,2,2,4,1]
[1,1,1,0,1,1,0,0,0,0] => 1110110000 => 1101100001 => [1,1,2,1,5,1]
[1,1,1,1,0,0,0,0,1,0] => 1111000010 => 1110000101 => [1,1,1,5,2,1]
[1,1,1,1,0,0,0,1,0,0] => 1111000100 => 1110001001 => [1,1,1,4,3,1]
[1,1,1,1,0,0,1,0,0,0] => 1111001000 => 1110010001 => [1,1,1,3,4,1]
[1,1,1,1,0,1,0,0,0,0] => 1111010000 => 1110100001 => [1,1,1,2,5,1]
[1,1,1,1,1,0,0,0,0,0] => 1111100000 => 1111000001 => [1,1,1,1,6,1]
[1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => 010101010101 => [2,2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,1,0,0] => 101010101100 => 010101011001 => [2,2,2,2,1,3,1]
[1,0,1,0,1,0,1,1,0,0,1,0] => 101010110010 => 010101100101 => [2,2,2,1,3,2,1]
[1,0,1,0,1,0,1,1,0,1,0,0] => 101010110100 => 010101101001 => [2,2,2,1,2,3,1]
[1,0,1,0,1,0,1,1,1,0,0,0] => 101010111000 => 010101110001 => [2,2,2,1,1,4,1]
[1,0,1,0,1,1,0,0,1,0,1,0] => 101011001010 => 010110010101 => [2,2,1,3,2,2,1]
[1,0,1,0,1,1,0,0,1,1,0,0] => 101011001100 => 010110011001 => [2,2,1,3,1,3,1]
[1,0,1,0,1,1,0,1,0,0,1,0] => 101011010010 => 010110100101 => [2,2,1,2,3,2,1]
[1,0,1,0,1,1,0,1,0,1,0,0] => 101011010100 => 010110101001 => [2,2,1,2,2,3,1]
[1,0,1,0,1,1,0,1,1,0,0,0] => 101011011000 => 010110110001 => [2,2,1,2,1,4,1]
[1,0,1,0,1,1,1,0,0,0,1,0] => 101011100010 => 010111000101 => [2,2,1,1,4,2,1]
[1,0,1,0,1,1,1,0,0,1,0,0] => 101011100100 => 010111001001 => [2,2,1,1,3,3,1]
[1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => 010111010001 => [2,2,1,1,2,4,1]
[1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 010111100001 => [2,2,1,1,1,5,1]
[1,0,1,1,0,0,1,0,1,0,1,0] => 101100101010 => 011001010101 => [2,1,3,2,2,2,1]
[1,0,1,1,0,0,1,0,1,1,0,0] => 101100101100 => 011001011001 => [2,1,3,2,1,3,1]
[1,0,1,1,0,0,1,1,0,0,1,0] => 101100110010 => 011001100101 => [2,1,3,1,3,2,1]
[1,0,1,1,0,0,1,1,0,1,0,0] => 101100110100 => 011001101001 => [2,1,3,1,2,3,1]
[1,0,1,1,0,0,1,1,1,0,0,0] => 101100111000 => 011001110001 => [2,1,3,1,1,4,1]
[1,0,1,1,0,1,0,0,1,0,1,0] => 101101001010 => 011010010101 => [2,1,2,3,2,2,1]
[1,0,1,1,0,1,0,0,1,1,0,0] => 101101001100 => 011010011001 => [2,1,2,3,1,3,1]
[1,0,1,1,0,1,0,1,0,0,1,0] => 101101010010 => 011010100101 => [2,1,2,2,3,2,1]
[1,0,1,1,0,1,0,1,0,1,0,0] => 101101010100 => 011010101001 => [2,1,2,2,2,3,1]
[1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 011010110001 => [2,1,2,2,1,4,1]
[1,0,1,1,0,1,1,0,0,0,1,0] => 101101100010 => 011011000101 => [2,1,2,1,4,2,1]
[1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => 011011001001 => [2,1,2,1,3,3,1]
[1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 011011010001 => [2,1,2,1,2,4,1]
[1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 011011100001 => [2,1,2,1,1,5,1]
[1,0,1,1,1,0,0,0,1,0,1,0] => 101110001010 => 011100010101 => [2,1,1,4,2,2,1]
[1,0,1,1,1,0,0,0,1,1,0,0] => 101110001100 => 011100011001 => [2,1,1,4,1,3,1]
[1,0,1,1,1,0,0,1,0,0,1,0] => 101110010010 => 011100100101 => [2,1,1,3,3,2,1]
[1,0,1,1,1,0,0,1,0,1,0,0] => 101110010100 => 011100101001 => [2,1,1,3,2,3,1]
[1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 011100110001 => [2,1,1,3,1,4,1]
[1,0,1,1,1,0,1,0,0,0,1,0] => 101110100010 => 011101000101 => [2,1,1,2,4,2,1]
[1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => 011101001001 => [2,1,1,2,3,3,1]
[1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 011101010001 => [2,1,1,2,2,4,1]
[1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 011101100001 => [2,1,1,2,1,5,1]
>>> Load all 204 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 011110000101 => [2,1,1,1,5,2,1]
[1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 011110001001 => [2,1,1,1,4,3,1]
[1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 011110010001 => [2,1,1,1,3,4,1]
[1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 011110100001 => [2,1,1,1,2,5,1]
[1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 011111000001 => [2,1,1,1,1,6,1]
[1,1,0,0,1,0,1,0,1,0,1,0] => 110010101010 => 100101010101 => [1,3,2,2,2,2,1]
[1,1,0,0,1,0,1,0,1,1,0,0] => 110010101100 => 100101011001 => [1,3,2,2,1,3,1]
[1,1,0,0,1,0,1,1,0,0,1,0] => 110010110010 => 100101100101 => [1,3,2,1,3,2,1]
[1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => 100101101001 => [1,3,2,1,2,3,1]
[1,1,0,0,1,0,1,1,1,0,0,0] => 110010111000 => 100101110001 => [1,3,2,1,1,4,1]
[1,1,0,0,1,1,0,0,1,0,1,0] => 110011001010 => 100110010101 => [1,3,1,3,2,2,1]
[1,1,0,0,1,1,0,0,1,1,0,0] => 110011001100 => 100110011001 => [1,3,1,3,1,3,1]
[1,1,0,0,1,1,0,1,0,0,1,0] => 110011010010 => 100110100101 => [1,3,1,2,3,2,1]
[1,1,0,0,1,1,0,1,0,1,0,0] => 110011010100 => 100110101001 => [1,3,1,2,2,3,1]
[1,1,0,0,1,1,0,1,1,0,0,0] => 110011011000 => 100110110001 => [1,3,1,2,1,4,1]
[1,1,0,0,1,1,1,0,0,0,1,0] => 110011100010 => 100111000101 => [1,3,1,1,4,2,1]
[1,1,0,0,1,1,1,0,0,1,0,0] => 110011100100 => 100111001001 => [1,3,1,1,3,3,1]
[1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => 100111010001 => [1,3,1,1,2,4,1]
[1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 100111100001 => [1,3,1,1,1,5,1]
[1,1,0,1,0,0,1,0,1,0,1,0] => 110100101010 => 101001010101 => [1,2,3,2,2,2,1]
[1,1,0,1,0,0,1,0,1,1,0,0] => 110100101100 => 101001011001 => [1,2,3,2,1,3,1]
[1,1,0,1,0,0,1,1,0,0,1,0] => 110100110010 => 101001100101 => [1,2,3,1,3,2,1]
[1,1,0,1,0,0,1,1,0,1,0,0] => 110100110100 => 101001101001 => [1,2,3,1,2,3,1]
[1,1,0,1,0,0,1,1,1,0,0,0] => 110100111000 => 101001110001 => [1,2,3,1,1,4,1]
[1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => 101010010101 => [1,2,2,3,2,2,1]
[1,1,0,1,0,1,0,0,1,1,0,0] => 110101001100 => 101010011001 => [1,2,2,3,1,3,1]
[1,1,0,1,0,1,0,1,0,0,1,0] => 110101010010 => 101010100101 => [1,2,2,2,3,2,1]
[1,1,0,1,0,1,0,1,0,1,0,0] => 110101010100 => 101010101001 => [1,2,2,2,2,3,1]
[1,1,0,1,0,1,0,1,1,0,0,0] => 110101011000 => 101010110001 => [1,2,2,2,1,4,1]
[1,1,0,1,0,1,1,0,0,0,1,0] => 110101100010 => 101011000101 => [1,2,2,1,4,2,1]
[1,1,0,1,0,1,1,0,0,1,0,0] => 110101100100 => 101011001001 => [1,2,2,1,3,3,1]
[1,1,0,1,0,1,1,0,1,0,0,0] => 110101101000 => 101011010001 => [1,2,2,1,2,4,1]
[1,1,0,1,0,1,1,1,0,0,0,0] => 110101110000 => 101011100001 => [1,2,2,1,1,5,1]
[1,1,0,1,1,0,0,0,1,0,1,0] => 110110001010 => 101100010101 => [1,2,1,4,2,2,1]
[1,1,0,1,1,0,0,0,1,1,0,0] => 110110001100 => 101100011001 => [1,2,1,4,1,3,1]
[1,1,0,1,1,0,0,1,0,0,1,0] => 110110010010 => 101100100101 => [1,2,1,3,3,2,1]
[1,1,0,1,1,0,0,1,0,1,0,0] => 110110010100 => 101100101001 => [1,2,1,3,2,3,1]
[1,1,0,1,1,0,0,1,1,0,0,0] => 110110011000 => 101100110001 => [1,2,1,3,1,4,1]
[1,1,0,1,1,0,1,0,0,0,1,0] => 110110100010 => 101101000101 => [1,2,1,2,4,2,1]
[1,1,0,1,1,0,1,0,0,1,0,0] => 110110100100 => 101101001001 => [1,2,1,2,3,3,1]
[1,1,0,1,1,0,1,0,1,0,0,0] => 110110101000 => 101101010001 => [1,2,1,2,2,4,1]
[1,1,0,1,1,0,1,1,0,0,0,0] => 110110110000 => 101101100001 => [1,2,1,2,1,5,1]
[1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 101110000101 => [1,2,1,1,5,2,1]
[1,1,0,1,1,1,0,0,0,1,0,0] => 110111000100 => 101110001001 => [1,2,1,1,4,3,1]
[1,1,0,1,1,1,0,0,1,0,0,0] => 110111001000 => 101110010001 => [1,2,1,1,3,4,1]
[1,1,0,1,1,1,0,1,0,0,0,0] => 110111010000 => 101110100001 => [1,2,1,1,2,5,1]
[1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 101111000001 => [1,2,1,1,1,6,1]
[1,1,1,0,0,0,1,0,1,0,1,0] => 111000101010 => 110001010101 => [1,1,4,2,2,2,1]
[1,1,1,0,0,0,1,0,1,1,0,0] => 111000101100 => 110001011001 => [1,1,4,2,1,3,1]
[1,1,1,0,0,0,1,1,0,0,1,0] => 111000110010 => 110001100101 => [1,1,4,1,3,2,1]
[1,1,1,0,0,0,1,1,0,1,0,0] => 111000110100 => 110001101001 => [1,1,4,1,2,3,1]
[1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 110001110001 => [1,1,4,1,1,4,1]
[1,1,1,0,0,1,0,0,1,0,1,0] => 111001001010 => 110010010101 => [1,1,3,3,2,2,1]
[1,1,1,0,0,1,0,0,1,1,0,0] => 111001001100 => 110010011001 => [1,1,3,3,1,3,1]
[1,1,1,0,0,1,0,1,0,0,1,0] => 111001010010 => 110010100101 => [1,1,3,2,3,2,1]
[1,1,1,0,0,1,0,1,0,1,0,0] => 111001010100 => 110010101001 => [1,1,3,2,2,3,1]
[1,1,1,0,0,1,0,1,1,0,0,0] => 111001011000 => 110010110001 => [1,1,3,2,1,4,1]
[1,1,1,0,0,1,1,0,0,0,1,0] => 111001100010 => 110011000101 => [1,1,3,1,4,2,1]
[1,1,1,0,0,1,1,0,0,1,0,0] => 111001100100 => 110011001001 => [1,1,3,1,3,3,1]
[1,1,1,0,0,1,1,0,1,0,0,0] => 111001101000 => 110011010001 => [1,1,3,1,2,4,1]
[1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 110011100001 => [1,1,3,1,1,5,1]
[1,1,1,0,1,0,0,0,1,0,1,0] => 111010001010 => 110100010101 => [1,1,2,4,2,2,1]
[1,1,1,0,1,0,0,0,1,1,0,0] => 111010001100 => 110100011001 => [1,1,2,4,1,3,1]
[1,1,1,0,1,0,0,1,0,0,1,0] => 111010010010 => 110100100101 => [1,1,2,3,3,2,1]
[1,1,1,0,1,0,0,1,0,1,0,0] => 111010010100 => 110100101001 => [1,1,2,3,2,3,1]
[1,1,1,0,1,0,0,1,1,0,0,0] => 111010011000 => 110100110001 => [1,1,2,3,1,4,1]
[1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => 110101000101 => [1,1,2,2,4,2,1]
[1,1,1,0,1,0,1,0,0,1,0,0] => 111010100100 => 110101001001 => [1,1,2,2,3,3,1]
[1,1,1,0,1,0,1,0,1,0,0,0] => 111010101000 => 110101010001 => [1,1,2,2,2,4,1]
[1,1,1,0,1,0,1,1,0,0,0,0] => 111010110000 => 110101100001 => [1,1,2,2,1,5,1]
[1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 110110000101 => [1,1,2,1,5,2,1]
[1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => 110110001001 => [1,1,2,1,4,3,1]
[1,1,1,0,1,1,0,0,1,0,0,0] => 111011001000 => 110110010001 => [1,1,2,1,3,4,1]
[1,1,1,0,1,1,0,1,0,0,0,0] => 111011010000 => 110110100001 => [1,1,2,1,2,5,1]
[1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 110111000001 => [1,1,2,1,1,6,1]
[1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 111000010101 => [1,1,1,5,2,2,1]
[1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 111000011001 => [1,1,1,5,1,3,1]
[1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 111000100101 => [1,1,1,4,3,2,1]
[1,1,1,1,0,0,0,1,0,1,0,0] => 111100010100 => 111000101001 => [1,1,1,4,2,3,1]
[1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 111000110001 => [1,1,1,4,1,4,1]
[1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 111001000101 => [1,1,1,3,4,2,1]
[1,1,1,1,0,0,1,0,0,1,0,0] => 111100100100 => 111001001001 => [1,1,1,3,3,3,1]
[1,1,1,1,0,0,1,0,1,0,0,0] => 111100101000 => 111001010001 => [1,1,1,3,2,4,1]
[1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 111001100001 => [1,1,1,3,1,5,1]
[1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 111010000101 => [1,1,1,2,5,2,1]
[1,1,1,1,0,1,0,0,0,1,0,0] => 111101000100 => 111010001001 => [1,1,1,2,4,3,1]
[1,1,1,1,0,1,0,0,1,0,0,0] => 111101001000 => 111010010001 => [1,1,1,2,3,4,1]
[1,1,1,1,0,1,0,1,0,0,0,0] => 111101010000 => 111010100001 => [1,1,1,2,2,5,1]
[1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 111011000001 => [1,1,1,2,1,6,1]
[1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 111100000101 => [1,1,1,1,6,2,1]
[1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 111100001001 => [1,1,1,1,5,3,1]
[1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 111100010001 => [1,1,1,1,4,4,1]
[1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 111100100001 => [1,1,1,1,3,5,1]
[1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 111101000001 => [1,1,1,1,2,6,1]
[1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 111110000001 => [1,1,1,1,1,7,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10101010101010 => 01010101010101 => [2,2,2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1010101010101010 => 0101010101010101 => [2,2,2,2,2,2,2,2,1]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => 1111011110000000 => 1110111100000001 => [1,1,1,2,1,1,1,8,1]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => 1111110110000000 => 1111101100000001 => [1,1,1,1,1,2,1,8,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 1111111100000000 => 1111111000000001 => [1,1,1,1,1,1,1,9,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010101010 => 010101010101010101 => [2,2,2,2,2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 10101010101010101010 => 01010101010101010101 => [2,2,2,2,2,2,2,2,2,2,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 11111111110000000000 => 11111111100000000001 => [1,1,1,1,1,1,1,1,1,11,1]
Map
to binary word
Description
Return the Dyck word as binary word.
Map
rotate front-to-back
Description
The rotation of a binary word, first letter last.
This is the word obtained by moving the first letter to the end.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.