Identifier
Mp00093: Dyck paths —to binary word⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Mp00280: Binary words —path rowmotion⟶ Binary words
Images
[1,0] => 10 => 01 => 10
[1,0,1,0] => 1010 => 0101 => 1010
[1,1,0,0] => 1100 => 1001 => 0110
[1,0,1,0,1,0] => 101010 => 010101 => 101010
[1,0,1,1,0,0] => 101100 => 011001 => 100110
[1,1,0,0,1,0] => 110010 => 100101 => 011010
[1,1,0,1,0,0] => 110100 => 101001 => 110010
[1,1,1,0,0,0] => 111000 => 110001 => 001110
[1,0,1,0,1,0,1,0] => 10101010 => 01010101 => 10101010
[1,0,1,0,1,1,0,0] => 10101100 => 01011001 => 10100110
[1,0,1,1,0,0,1,0] => 10110010 => 01100101 => 10011010
[1,0,1,1,0,1,0,0] => 10110100 => 01101001 => 10110010
[1,0,1,1,1,0,0,0] => 10111000 => 01110001 => 10001110
[1,1,0,0,1,0,1,0] => 11001010 => 10010101 => 01101010
[1,1,0,0,1,1,0,0] => 11001100 => 10011001 => 01100110
[1,1,0,1,0,0,1,0] => 11010010 => 10100101 => 11001010
[1,1,0,1,0,1,0,0] => 11010100 => 10101001 => 11010010
[1,1,0,1,1,0,0,0] => 11011000 => 10110001 => 11000110
[1,1,1,0,0,0,1,0] => 11100010 => 11000101 => 00111010
[1,1,1,0,0,1,0,0] => 11100100 => 11001001 => 01110010
[1,1,1,0,1,0,0,0] => 11101000 => 11010001 => 11100010
[1,1,1,1,0,0,0,0] => 11110000 => 11100001 => 00011110
[1,0,1,0,1,0,1,0,1,0] => 1010101010 => 0101010101 => 1010101010
[1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0101011001 => 1010100110
[1,0,1,0,1,1,0,0,1,0] => 1010110010 => 0101100101 => 1010011010
[1,0,1,0,1,1,0,1,0,0] => 1010110100 => 0101101001 => 1010110010
[1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0101110001 => 1010001110
[1,0,1,1,0,0,1,0,1,0] => 1011001010 => 0110010101 => 1001101010
[1,0,1,1,0,0,1,1,0,0] => 1011001100 => 0110011001 => 1001100110
[1,0,1,1,0,1,0,0,1,0] => 1011010010 => 0110100101 => 1011001010
[1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0110101001 => 1011010010
[1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0110110001 => 1011000110
[1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0111000101 => 1000111010
[1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0111001001 => 1001110010
[1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0111010001 => 1011100010
[1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0111100001 => 1000011110
[1,1,0,0,1,0,1,0,1,0] => 1100101010 => 1001010101 => 0110101010
[1,1,0,0,1,0,1,1,0,0] => 1100101100 => 1001011001 => 0110100110
[1,1,0,0,1,1,0,0,1,0] => 1100110010 => 1001100101 => 0110011010
[1,1,0,0,1,1,0,1,0,0] => 1100110100 => 1001101001 => 0110110010
[1,1,0,0,1,1,1,0,0,0] => 1100111000 => 1001110001 => 0110001110
[1,1,0,1,0,0,1,0,1,0] => 1101001010 => 1010010101 => 1100101010
[1,1,0,1,0,0,1,1,0,0] => 1101001100 => 1010011001 => 1100100110
[1,1,0,1,0,1,0,0,1,0] => 1101010010 => 1010100101 => 1101001010
[1,1,0,1,0,1,0,1,0,0] => 1101010100 => 1010101001 => 1101010010
[1,1,0,1,0,1,1,0,0,0] => 1101011000 => 1010110001 => 1101000110
[1,1,0,1,1,0,0,0,1,0] => 1101100010 => 1011000101 => 1100011010
[1,1,0,1,1,0,0,1,0,0] => 1101100100 => 1011001001 => 1100110010
[1,1,0,1,1,0,1,0,0,0] => 1101101000 => 1011010001 => 1101100010
[1,1,0,1,1,1,0,0,0,0] => 1101110000 => 1011100001 => 1100001110
[1,1,1,0,0,0,1,0,1,0] => 1110001010 => 1100010101 => 0011101010
[1,1,1,0,0,0,1,1,0,0] => 1110001100 => 1100011001 => 0011100110
[1,1,1,0,0,1,0,0,1,0] => 1110010010 => 1100100101 => 0111001010
[1,1,1,0,0,1,0,1,0,0] => 1110010100 => 1100101001 => 0111010010
[1,1,1,0,0,1,1,0,0,0] => 1110011000 => 1100110001 => 0111000110
[1,1,1,0,1,0,0,0,1,0] => 1110100010 => 1101000101 => 1110001010
[1,1,1,0,1,0,0,1,0,0] => 1110100100 => 1101001001 => 1110010010
[1,1,1,0,1,0,1,0,0,0] => 1110101000 => 1101010001 => 1110100010
[1,1,1,0,1,1,0,0,0,0] => 1110110000 => 1101100001 => 1110000110
[1,1,1,1,0,0,0,0,1,0] => 1111000010 => 1110000101 => 0001111010
[1,1,1,1,0,0,0,1,0,0] => 1111000100 => 1110001001 => 0011110010
[1,1,1,1,0,0,1,0,0,0] => 1111001000 => 1110010001 => 0111100010
[1,1,1,1,0,1,0,0,0,0] => 1111010000 => 1110100001 => 1111000010
[1,1,1,1,1,0,0,0,0,0] => 1111100000 => 1111000001 => 0000111110
[1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => 010101010101 => 101010101010
[1,0,1,0,1,0,1,0,1,1,0,0] => 101010101100 => 010101011001 => 101010100110
[1,0,1,0,1,0,1,1,0,0,1,0] => 101010110010 => 010101100101 => 101010011010
[1,0,1,0,1,0,1,1,0,1,0,0] => 101010110100 => 010101101001 => 101010110010
[1,0,1,0,1,0,1,1,1,0,0,0] => 101010111000 => 010101110001 => 101010001110
[1,0,1,0,1,1,0,0,1,0,1,0] => 101011001010 => 010110010101 => 101001101010
[1,0,1,0,1,1,0,0,1,1,0,0] => 101011001100 => 010110011001 => 101001100110
[1,0,1,0,1,1,0,1,0,0,1,0] => 101011010010 => 010110100101 => 101011001010
[1,0,1,0,1,1,0,1,0,1,0,0] => 101011010100 => 010110101001 => 101011010010
[1,0,1,0,1,1,0,1,1,0,0,0] => 101011011000 => 010110110001 => 101011000110
[1,0,1,0,1,1,1,0,0,0,1,0] => 101011100010 => 010111000101 => 101000111010
[1,0,1,0,1,1,1,0,0,1,0,0] => 101011100100 => 010111001001 => 101001110010
[1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => 010111010001 => 101011100010
[1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 010111100001 => 101000011110
[1,0,1,1,0,0,1,0,1,0,1,0] => 101100101010 => 011001010101 => 100110101010
[1,0,1,1,0,0,1,0,1,1,0,0] => 101100101100 => 011001011001 => 100110100110
[1,0,1,1,0,0,1,1,0,0,1,0] => 101100110010 => 011001100101 => 100110011010
[1,0,1,1,0,0,1,1,0,1,0,0] => 101100110100 => 011001101001 => 100110110010
[1,0,1,1,0,0,1,1,1,0,0,0] => 101100111000 => 011001110001 => 100110001110
[1,0,1,1,0,1,0,0,1,0,1,0] => 101101001010 => 011010010101 => 101100101010
[1,0,1,1,0,1,0,0,1,1,0,0] => 101101001100 => 011010011001 => 101100100110
[1,0,1,1,0,1,0,1,0,0,1,0] => 101101010010 => 011010100101 => 101101001010
[1,0,1,1,0,1,0,1,0,1,0,0] => 101101010100 => 011010101001 => 101101010010
[1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 011010110001 => 101101000110
[1,0,1,1,0,1,1,0,0,0,1,0] => 101101100010 => 011011000101 => 101100011010
[1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => 011011001001 => 101100110010
[1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 011011010001 => 101101100010
[1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 011011100001 => 101100001110
[1,0,1,1,1,0,0,0,1,0,1,0] => 101110001010 => 011100010101 => 100011101010
[1,0,1,1,1,0,0,0,1,1,0,0] => 101110001100 => 011100011001 => 100011100110
[1,0,1,1,1,0,0,1,0,0,1,0] => 101110010010 => 011100100101 => 100111001010
[1,0,1,1,1,0,0,1,0,1,0,0] => 101110010100 => 011100101001 => 100111010010
[1,0,1,1,1,0,0,1,1,0,0,0] => 101110011000 => 011100110001 => 100111000110
[1,0,1,1,1,0,1,0,0,0,1,0] => 101110100010 => 011101000101 => 101110001010
[1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => 011101001001 => 101110010010
[1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 011101010001 => 101110100010
[1,0,1,1,1,0,1,1,0,0,0,0] => 101110110000 => 011101100001 => 101110000110
>>> Load all 196 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 011110000101 => 100001111010
[1,0,1,1,1,1,0,0,0,1,0,0] => 101111000100 => 011110001001 => 100011110010
[1,0,1,1,1,1,0,0,1,0,0,0] => 101111001000 => 011110010001 => 100111100010
[1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 011110100001 => 101111000010
[1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 011111000001 => 100000111110
[1,1,0,0,1,0,1,0,1,0,1,0] => 110010101010 => 100101010101 => 011010101010
[1,1,0,0,1,0,1,0,1,1,0,0] => 110010101100 => 100101011001 => 011010100110
[1,1,0,0,1,0,1,1,0,0,1,0] => 110010110010 => 100101100101 => 011010011010
[1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => 100101101001 => 011010110010
[1,1,0,0,1,0,1,1,1,0,0,0] => 110010111000 => 100101110001 => 011010001110
[1,1,0,0,1,1,0,0,1,0,1,0] => 110011001010 => 100110010101 => 011001101010
[1,1,0,0,1,1,0,0,1,1,0,0] => 110011001100 => 100110011001 => 011001100110
[1,1,0,0,1,1,0,1,0,0,1,0] => 110011010010 => 100110100101 => 011011001010
[1,1,0,0,1,1,0,1,0,1,0,0] => 110011010100 => 100110101001 => 011011010010
[1,1,0,0,1,1,0,1,1,0,0,0] => 110011011000 => 100110110001 => 011011000110
[1,1,0,0,1,1,1,0,0,0,1,0] => 110011100010 => 100111000101 => 011000111010
[1,1,0,0,1,1,1,0,0,1,0,0] => 110011100100 => 100111001001 => 011001110010
[1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => 100111010001 => 011011100010
[1,1,0,0,1,1,1,1,0,0,0,0] => 110011110000 => 100111100001 => 011000011110
[1,1,0,1,0,0,1,0,1,0,1,0] => 110100101010 => 101001010101 => 110010101010
[1,1,0,1,0,0,1,0,1,1,0,0] => 110100101100 => 101001011001 => 110010100110
[1,1,0,1,0,0,1,1,0,0,1,0] => 110100110010 => 101001100101 => 110010011010
[1,1,0,1,0,0,1,1,0,1,0,0] => 110100110100 => 101001101001 => 110010110010
[1,1,0,1,0,0,1,1,1,0,0,0] => 110100111000 => 101001110001 => 110010001110
[1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => 101010010101 => 110100101010
[1,1,0,1,0,1,0,0,1,1,0,0] => 110101001100 => 101010011001 => 110100100110
[1,1,0,1,0,1,0,1,0,0,1,0] => 110101010010 => 101010100101 => 110101001010
[1,1,0,1,0,1,0,1,0,1,0,0] => 110101010100 => 101010101001 => 110101010010
[1,1,0,1,0,1,0,1,1,0,0,0] => 110101011000 => 101010110001 => 110101000110
[1,1,0,1,0,1,1,0,0,0,1,0] => 110101100010 => 101011000101 => 110100011010
[1,1,0,1,0,1,1,0,0,1,0,0] => 110101100100 => 101011001001 => 110100110010
[1,1,0,1,0,1,1,0,1,0,0,0] => 110101101000 => 101011010001 => 110101100010
[1,1,0,1,0,1,1,1,0,0,0,0] => 110101110000 => 101011100001 => 110100001110
[1,1,0,1,1,0,0,0,1,0,1,0] => 110110001010 => 101100010101 => 110001101010
[1,1,0,1,1,0,0,0,1,1,0,0] => 110110001100 => 101100011001 => 110001100110
[1,1,0,1,1,0,0,1,0,0,1,0] => 110110010010 => 101100100101 => 110011001010
[1,1,0,1,1,0,0,1,0,1,0,0] => 110110010100 => 101100101001 => 110011010010
[1,1,0,1,1,0,0,1,1,0,0,0] => 110110011000 => 101100110001 => 110011000110
[1,1,0,1,1,0,1,0,0,0,1,0] => 110110100010 => 101101000101 => 110110001010
[1,1,0,1,1,0,1,0,0,1,0,0] => 110110100100 => 101101001001 => 110110010010
[1,1,0,1,1,0,1,0,1,0,0,0] => 110110101000 => 101101010001 => 110110100010
[1,1,0,1,1,0,1,1,0,0,0,0] => 110110110000 => 101101100001 => 110110000110
[1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 101110000101 => 110000111010
[1,1,0,1,1,1,0,0,0,1,0,0] => 110111000100 => 101110001001 => 110001110010
[1,1,0,1,1,1,0,0,1,0,0,0] => 110111001000 => 101110010001 => 110011100010
[1,1,0,1,1,1,0,1,0,0,0,0] => 110111010000 => 101110100001 => 110111000010
[1,1,0,1,1,1,1,0,0,0,0,0] => 110111100000 => 101111000001 => 110000011110
[1,1,1,0,0,0,1,0,1,0,1,0] => 111000101010 => 110001010101 => 001110101010
[1,1,1,0,0,0,1,0,1,1,0,0] => 111000101100 => 110001011001 => 001110100110
[1,1,1,0,0,0,1,1,0,0,1,0] => 111000110010 => 110001100101 => 001110011010
[1,1,1,0,0,0,1,1,0,1,0,0] => 111000110100 => 110001101001 => 001110110010
[1,1,1,0,0,0,1,1,1,0,0,0] => 111000111000 => 110001110001 => 001110001110
[1,1,1,0,0,1,0,0,1,0,1,0] => 111001001010 => 110010010101 => 011100101010
[1,1,1,0,0,1,0,0,1,1,0,0] => 111001001100 => 110010011001 => 011100100110
[1,1,1,0,0,1,0,1,0,0,1,0] => 111001010010 => 110010100101 => 011101001010
[1,1,1,0,0,1,0,1,0,1,0,0] => 111001010100 => 110010101001 => 011101010010
[1,1,1,0,0,1,0,1,1,0,0,0] => 111001011000 => 110010110001 => 011101000110
[1,1,1,0,0,1,1,0,0,0,1,0] => 111001100010 => 110011000101 => 011100011010
[1,1,1,0,0,1,1,0,0,1,0,0] => 111001100100 => 110011001001 => 011100110010
[1,1,1,0,0,1,1,0,1,0,0,0] => 111001101000 => 110011010001 => 011101100010
[1,1,1,0,0,1,1,1,0,0,0,0] => 111001110000 => 110011100001 => 011100001110
[1,1,1,0,1,0,0,0,1,0,1,0] => 111010001010 => 110100010101 => 111000101010
[1,1,1,0,1,0,0,0,1,1,0,0] => 111010001100 => 110100011001 => 111000100110
[1,1,1,0,1,0,0,1,0,0,1,0] => 111010010010 => 110100100101 => 111001001010
[1,1,1,0,1,0,0,1,0,1,0,0] => 111010010100 => 110100101001 => 111001010010
[1,1,1,0,1,0,0,1,1,0,0,0] => 111010011000 => 110100110001 => 111001000110
[1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => 110101000101 => 111010001010
[1,1,1,0,1,0,1,0,0,1,0,0] => 111010100100 => 110101001001 => 111010010010
[1,1,1,0,1,0,1,0,1,0,0,0] => 111010101000 => 110101010001 => 111010100010
[1,1,1,0,1,0,1,1,0,0,0,0] => 111010110000 => 110101100001 => 111010000110
[1,1,1,0,1,1,0,0,0,0,1,0] => 111011000010 => 110110000101 => 111000011010
[1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => 110110001001 => 111000110010
[1,1,1,0,1,1,0,0,1,0,0,0] => 111011001000 => 110110010001 => 111001100010
[1,1,1,0,1,1,0,1,0,0,0,0] => 111011010000 => 110110100001 => 111011000010
[1,1,1,0,1,1,1,0,0,0,0,0] => 111011100000 => 110111000001 => 111000001110
[1,1,1,1,0,0,0,0,1,0,1,0] => 111100001010 => 111000010101 => 000111101010
[1,1,1,1,0,0,0,0,1,1,0,0] => 111100001100 => 111000011001 => 000111100110
[1,1,1,1,0,0,0,1,0,0,1,0] => 111100010010 => 111000100101 => 001111001010
[1,1,1,1,0,0,0,1,0,1,0,0] => 111100010100 => 111000101001 => 001111010010
[1,1,1,1,0,0,0,1,1,0,0,0] => 111100011000 => 111000110001 => 001111000110
[1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 111001000101 => 011110001010
[1,1,1,1,0,0,1,0,0,1,0,0] => 111100100100 => 111001001001 => 011110010010
[1,1,1,1,0,0,1,0,1,0,0,0] => 111100101000 => 111001010001 => 011110100010
[1,1,1,1,0,0,1,1,0,0,0,0] => 111100110000 => 111001100001 => 011110000110
[1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 111010000101 => 111100001010
[1,1,1,1,0,1,0,0,0,1,0,0] => 111101000100 => 111010001001 => 111100010010
[1,1,1,1,0,1,0,0,1,0,0,0] => 111101001000 => 111010010001 => 111100100010
[1,1,1,1,0,1,0,1,0,0,0,0] => 111101010000 => 111010100001 => 111101000010
[1,1,1,1,0,1,1,0,0,0,0,0] => 111101100000 => 111011000001 => 111100000110
[1,1,1,1,1,0,0,0,0,0,1,0] => 111110000010 => 111100000101 => 000011111010
[1,1,1,1,1,0,0,0,0,1,0,0] => 111110000100 => 111100001001 => 000111110010
[1,1,1,1,1,0,0,0,1,0,0,0] => 111110001000 => 111100010001 => 001111100010
[1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 111100100001 => 011111000010
[1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 111101000001 => 111110000010
[1,1,1,1,1,1,0,0,0,0,0,0] => 111111000000 => 111110000001 => 000001111110
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
path rowmotion
Description
Return the rowmotion of the binary word, regarded as a lattice path.
Consider the binary word of length $n$ as a lattice path with $n$ steps, where a 1 corresponds to an up step and a 0 corresponds to a down step.
This map returns the path whose peaks are the valleys of the original path with an up step appended.