Identifier
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Mp00280: Binary words —path rowmotion⟶ Binary words
Images
[1] => 10 => 01 => 10
[2] => 100 => 001 => 010
[1,1] => 110 => 101 => 110
[3] => 1000 => 0001 => 0010
[2,1] => 1010 => 0101 => 1010
[1,1,1] => 1110 => 1101 => 1110
[4] => 10000 => 00001 => 00010
[3,1] => 10010 => 00101 => 01010
[2,2] => 1100 => 1001 => 0110
[2,1,1] => 10110 => 01101 => 10110
[1,1,1,1] => 11110 => 11101 => 11110
[5] => 100000 => 000001 => 000010
[4,1] => 100010 => 000101 => 001010
[3,2] => 10100 => 01001 => 10010
[3,1,1] => 100110 => 001101 => 010110
[2,2,1] => 11010 => 10101 => 11010
[2,1,1,1] => 101110 => 011101 => 101110
[1,1,1,1,1] => 111110 => 111101 => 111110
[6] => 1000000 => 0000001 => 0000010
[5,1] => 1000010 => 0000101 => 0001010
[4,2] => 100100 => 001001 => 010010
[4,1,1] => 1000110 => 0001101 => 0010110
[3,3] => 11000 => 10001 => 00110
[3,2,1] => 101010 => 010101 => 101010
[3,1,1,1] => 1001110 => 0011101 => 0101110
[2,2,2] => 11100 => 11001 => 01110
[2,2,1,1] => 110110 => 101101 => 110110
[2,1,1,1,1] => 1011110 => 0111101 => 1011110
[1,1,1,1,1,1] => 1111110 => 1111101 => 1111110
[7] => 10000000 => 00000001 => 00000010
[6,1] => 10000010 => 00000101 => 00001010
[5,2] => 1000100 => 0001001 => 0010010
[5,1,1] => 10000110 => 00001101 => 00010110
[4,3] => 101000 => 010001 => 100010
[4,2,1] => 1001010 => 0010101 => 0101010
[4,1,1,1] => 10001110 => 00011101 => 00101110
[3,3,1] => 110010 => 100101 => 011010
[3,2,2] => 101100 => 011001 => 100110
[3,2,1,1] => 1010110 => 0101101 => 1010110
[3,1,1,1,1] => 10011110 => 00111101 => 01011110
[2,2,2,1] => 111010 => 110101 => 111010
[2,2,1,1,1] => 1101110 => 1011101 => 1101110
[2,1,1,1,1,1] => 10111110 => 01111101 => 10111110
[1,1,1,1,1,1,1] => 11111110 => 11111101 => 11111110
[8] => 100000000 => 000000001 => 000000010
[7,1] => 100000010 => 000000101 => 000001010
[6,2] => 10000100 => 00001001 => 00010010
[6,1,1] => 100000110 => 000001101 => 000010110
[5,3] => 1001000 => 0010001 => 0100010
[5,2,1] => 10001010 => 00010101 => 00101010
[5,1,1,1] => 100001110 => 000011101 => 000101110
[4,4] => 110000 => 100001 => 000110
[4,3,1] => 1010010 => 0100101 => 1001010
[4,2,2] => 1001100 => 0011001 => 0100110
[4,2,1,1] => 10010110 => 00101101 => 01010110
[4,1,1,1,1] => 100011110 => 000111101 => 001011110
[3,3,2] => 110100 => 101001 => 110010
[3,3,1,1] => 1100110 => 1001101 => 0110110
[3,2,2,1] => 1011010 => 0110101 => 1011010
[3,2,1,1,1] => 10101110 => 01011101 => 10101110
[3,1,1,1,1,1] => 100111110 => 001111101 => 010111110
[2,2,2,2] => 111100 => 111001 => 011110
[2,2,2,1,1] => 1110110 => 1101101 => 1110110
[2,2,1,1,1,1] => 11011110 => 10111101 => 11011110
[2,1,1,1,1,1,1] => 101111110 => 011111101 => 101111110
[1,1,1,1,1,1,1,1] => 111111110 => 111111101 => 111111110
[9] => 1000000000 => 0000000001 => 0000000010
[8,1] => 1000000010 => 0000000101 => 0000001010
[7,2] => 100000100 => 000001001 => 000010010
[7,1,1] => 1000000110 => 0000001101 => 0000010110
[6,3] => 10001000 => 00010001 => 00100010
[6,2,1] => 100001010 => 000010101 => 000101010
[6,1,1,1] => 1000001110 => 0000011101 => 0000101110
[5,4] => 1010000 => 0100001 => 1000010
[5,3,1] => 10010010 => 00100101 => 01001010
[5,2,2] => 10001100 => 00011001 => 00100110
[5,2,1,1] => 100010110 => 000101101 => 001010110
[5,1,1,1,1] => 1000011110 => 0000111101 => 0001011110
[4,4,1] => 1100010 => 1000101 => 0011010
[4,3,2] => 1010100 => 0101001 => 1010010
[4,3,1,1] => 10100110 => 01001101 => 10010110
[4,2,2,1] => 10011010 => 00110101 => 01011010
[4,2,1,1,1] => 100101110 => 001011101 => 010101110
[4,1,1,1,1,1] => 1000111110 => 0001111101 => 0010111110
[3,3,3] => 111000 => 110001 => 001110
[3,3,2,1] => 1101010 => 1010101 => 1101010
[3,3,1,1,1] => 11001110 => 10011101 => 01101110
[3,2,2,2] => 1011100 => 0111001 => 1001110
[3,2,2,1,1] => 10110110 => 01101101 => 10110110
[3,2,1,1,1,1] => 101011110 => 010111101 => 101011110
[3,1,1,1,1,1,1] => 1001111110 => 0011111101 => 0101111110
[2,2,2,2,1] => 1111010 => 1110101 => 1111010
[2,2,2,1,1,1] => 11101110 => 11011101 => 11101110
[2,2,1,1,1,1,1] => 110111110 => 101111101 => 110111110
[2,1,1,1,1,1,1,1] => 1011111110 => 0111111101 => 1011111110
[1,1,1,1,1,1,1,1,1] => 1111111110 => 1111111101 => 1111111110
[10] => 10000000000 => 00000000001 => 00000000010
[9,1] => 10000000010 => 00000000101 => 00000001010
[8,2] => 1000000100 => 0000001001 => 0000010010
[8,1,1] => 10000000110 => 00000001101 => 00000010110
[7,3] => 100001000 => 000010001 => 000100010
>>> Load all 397 entries. <<<
[7,2,1] => 1000001010 => 0000010101 => 0000101010
[7,1,1,1] => 10000001110 => 00000011101 => 00000101110
[6,4] => 10010000 => 00100001 => 01000010
[6,3,1] => 100010010 => 000100101 => 001001010
[6,2,2] => 100001100 => 000011001 => 000100110
[6,2,1,1] => 1000010110 => 0000101101 => 0001010110
[6,1,1,1,1] => 10000011110 => 00000111101 => 00001011110
[5,5] => 1100000 => 1000001 => 0000110
[5,4,1] => 10100010 => 01000101 => 10001010
[5,3,2] => 10010100 => 00101001 => 01010010
[5,3,1,1] => 100100110 => 001001101 => 010010110
[5,2,2,1] => 100011010 => 000110101 => 001011010
[5,2,1,1,1] => 1000101110 => 0001011101 => 0010101110
[5,1,1,1,1,1] => 10000111110 => 00001111101 => 00010111110
[4,4,2] => 1100100 => 1001001 => 0110010
[4,4,1,1] => 11000110 => 10001101 => 00110110
[4,3,3] => 1011000 => 0110001 => 1000110
[4,3,2,1] => 10101010 => 01010101 => 10101010
[4,3,1,1,1] => 101001110 => 010011101 => 100101110
[4,2,2,2] => 10011100 => 00111001 => 01001110
[4,2,2,1,1] => 100110110 => 001101101 => 010110110
[4,2,1,1,1,1] => 1001011110 => 0010111101 => 0101011110
[4,1,1,1,1,1,1] => 10001111110 => 00011111101 => 00101111110
[3,3,3,1] => 1110010 => 1100101 => 0111010
[3,3,2,2] => 1101100 => 1011001 => 1100110
[3,3,2,1,1] => 11010110 => 10101101 => 11010110
[3,3,1,1,1,1] => 110011110 => 100111101 => 011011110
[3,2,2,2,1] => 10111010 => 01110101 => 10111010
[3,2,2,1,1,1] => 101101110 => 011011101 => 101101110
[3,2,1,1,1,1,1] => 1010111110 => 0101111101 => 1010111110
[3,1,1,1,1,1,1,1] => 10011111110 => 00111111101 => 01011111110
[2,2,2,2,2] => 1111100 => 1111001 => 0111110
[2,2,2,2,1,1] => 11110110 => 11101101 => 11110110
[2,2,2,1,1,1,1] => 111011110 => 110111101 => 111011110
[2,2,1,1,1,1,1,1] => 1101111110 => 1011111101 => 1101111110
[2,1,1,1,1,1,1,1,1] => 10111111110 => 01111111101 => 10111111110
[1,1,1,1,1,1,1,1,1,1] => 11111111110 => 11111111101 => 11111111110
[7,4] => 100010000 => 000100001 => 001000010
[6,5] => 10100000 => 01000001 => 10000010
[6,4,1] => 100100010 => 001000101 => 010001010
[6,3,2] => 100010100 => 000101001 => 001010010
[6,1,1,1,1,1] => 100000111110 => 000001111101 => 000010111110
[5,5,1] => 11000010 => 10000101 => 00011010
[5,4,2] => 10100100 => 01001001 => 10010010
[5,4,1,1] => 101000110 => 010001101 => 100010110
[5,3,3] => 10011000 => 00110001 => 01000110
[5,3,2,1] => 100101010 => 001010101 => 010101010
[5,3,1,1,1] => 1001001110 => 0010011101 => 0100101110
[5,2,2,2] => 100011100 => 000111001 => 001001110
[5,2,2,1,1] => 1000110110 => 0001101101 => 0010110110
[4,4,3] => 1101000 => 1010001 => 1100010
[4,4,2,1] => 11001010 => 10010101 => 01101010
[4,4,1,1,1] => 110001110 => 100011101 => 001101110
[4,3,3,1] => 10110010 => 01100101 => 10011010
[4,3,2,2] => 10101100 => 01011001 => 10100110
[4,3,2,1,1] => 101010110 => 010101101 => 101010110
[4,2,2,2,1] => 100111010 => 001110101 => 010111010
[3,3,3,2] => 1110100 => 1101001 => 1110010
[3,3,3,1,1] => 11100110 => 11001101 => 01110110
[3,3,2,2,1] => 11011010 => 10110101 => 11011010
[3,3,2,1,1,1] => 110101110 => 101011101 => 110101110
[3,2,2,2,2] => 10111100 => 01111001 => 10011110
[3,2,2,2,1,1] => 101110110 => 011101101 => 101110110
[2,2,2,2,2,1] => 11111010 => 11110101 => 11111010
[2,2,2,2,1,1,1] => 111101110 => 111011101 => 111101110
[7,5] => 100100000 => 001000001 => 010000010
[6,6] => 11000000 => 10000001 => 00000110
[6,5,1] => 101000010 => 010000101 => 100001010
[6,4,2] => 100100100 => 001001001 => 010010010
[6,3,3] => 100011000 => 000110001 => 001000110
[6,2,1,1,1,1] => 100001011110 => 000010111101 => 000101011110
[5,5,2] => 11000100 => 10001001 => 00110010
[5,5,1,1] => 110000110 => 100001101 => 000110110
[5,4,3] => 10101000 => 01010001 => 10100010
[5,4,2,1] => 101001010 => 010010101 => 100101010
[5,4,1,1,1] => 1010001110 => 0100011101 => 1000101110
[5,3,3,1] => 100110010 => 001100101 => 010011010
[5,3,2,2] => 100101100 => 001011001 => 010100110
[5,3,2,1,1] => 1001010110 => 0010101101 => 0101010110
[5,2,2,2,1] => 1000111010 => 0001110101 => 0010111010
[4,4,4] => 1110000 => 1100001 => 0001110
[4,4,3,1] => 11010010 => 10100101 => 11001010
[4,4,2,2] => 11001100 => 10011001 => 01100110
[4,4,2,1,1] => 110010110 => 100101101 => 011010110
[4,4,1,1,1,1] => 1100011110 => 1000111101 => 0011011110
[4,3,3,2] => 10110100 => 01101001 => 10110010
[4,3,3,1,1] => 101100110 => 011001101 => 100110110
[4,3,2,2,1] => 101011010 => 010110101 => 101011010
[4,2,2,2,2] => 100111100 => 001111001 => 010011110
[3,3,3,3] => 1111000 => 1110001 => 0011110
[3,3,3,2,1] => 11101010 => 11010101 => 11101010
[3,3,3,1,1,1] => 111001110 => 110011101 => 011101110
[3,3,2,2,2] => 11011100 => 10111001 => 11001110
[3,3,2,2,1,1] => 110110110 => 101101101 => 110110110
[3,2,2,2,2,1] => 101111010 => 011110101 => 101111010
[2,2,2,2,2,2] => 11111100 => 11111001 => 01111110
[2,2,2,2,2,1,1] => 111110110 => 111101101 => 111110110
[7,6] => 101000000 => 010000001 => 100000010
[6,6,1] => 110000010 => 100000101 => 000011010
[6,5,2] => 101000100 => 010001001 => 100010010
[6,4,3] => 100101000 => 001010001 => 010100010
[6,3,1,1,1,1] => 100010011110 => 000100111101 => 001001011110
[6,2,2,1,1,1] => 100001101110 => 000011011101 => 000101101110
[5,5,3] => 11001000 => 10010001 => 01100010
[5,5,2,1] => 110001010 => 100010101 => 001101010
[5,4,4] => 10110000 => 01100001 => 10000110
[5,4,3,1] => 101010010 => 010100101 => 101001010
[5,4,2,2] => 101001100 => 010011001 => 100100110
[5,4,2,1,1] => 1010010110 => 0100101101 => 1001010110
[5,3,3,2] => 100110100 => 001101001 => 010110010
[5,3,3,1,1] => 1001100110 => 0011001101 => 0100110110
[5,3,2,2,1] => 1001011010 => 0010110101 => 0101011010
[4,4,4,1] => 11100010 => 11000101 => 00111010
[4,4,3,2] => 11010100 => 10101001 => 11010010
[4,4,3,1,1] => 110100110 => 101001101 => 110010110
[4,4,2,2,1] => 110011010 => 100110101 => 011011010
[4,3,3,3] => 10111000 => 01110001 => 10001110
[4,3,3,2,1] => 101101010 => 011010101 => 101101010
[4,3,2,2,2] => 101011100 => 010111001 => 101001110
[3,3,3,3,1] => 11110010 => 11100101 => 01111010
[3,3,3,2,2] => 11101100 => 11011001 => 11100110
[3,3,3,2,1,1] => 111010110 => 110101101 => 111010110
[3,3,2,2,2,1] => 110111010 => 101110101 => 110111010
[3,2,2,2,2,2] => 101111100 => 011111001 => 100111110
[2,2,2,2,2,2,1] => 111111010 => 111110101 => 111111010
[8,6] => 1001000000 => 0010000001 => 0100000010
[8,5,1] => 10001000010 => 00010000101 => 00100001010
[7,7] => 110000000 => 100000001 => 000000110
[7,6,1] => 1010000010 => 0100000101 => 1000001010
[6,6,2] => 110000100 => 100001001 => 000110010
[6,6,1,1] => 1100000110 => 1000001101 => 0000110110
[6,5,3] => 101001000 => 010010001 => 100100010
[6,4,4] => 100110000 => 001100001 => 010000110
[6,4,1,1,1,1] => 100100011110 => 001000111101 => 010001011110
[6,3,2,1,1,1] => 100010101110 => 000101011101 => 001010101110
[6,2,2,2,1,1] => 100001110110 => 000011101101 => 000101110110
[5,5,4] => 11010000 => 10100001 => 11000010
[5,5,3,1] => 110010010 => 100100101 => 011001010
[5,5,2,2] => 110001100 => 100011001 => 001100110
[5,4,4,1] => 101100010 => 011000101 => 100011010
[5,4,3,2] => 101010100 => 010101001 => 101010010
[5,4,3,1,1] => 1010100110 => 0101001101 => 1010010110
[5,4,2,2,1] => 1010011010 => 0100110101 => 1001011010
[5,3,3,3] => 100111000 => 001110001 => 010001110
[5,3,3,2,1] => 1001101010 => 0011010101 => 0101101010
[4,4,4,2] => 11100100 => 11001001 => 01110010
[4,4,4,1,1] => 111000110 => 110001101 => 001110110
[4,4,3,3] => 11011000 => 10110001 => 11000110
[4,4,3,2,1] => 110101010 => 101010101 => 110101010
[4,4,3,1,1,1] => 1101001110 => 1010011101 => 1100101110
[4,4,2,2,2] => 110011100 => 100111001 => 011001110
[4,3,3,3,1] => 101110010 => 011100101 => 100111010
[4,3,3,2,2] => 101101100 => 011011001 => 101100110
[3,3,3,3,2] => 11110100 => 11101001 => 11110010
[3,3,3,3,1,1] => 111100110 => 111001101 => 011110110
[3,3,3,2,2,1] => 111011010 => 110110101 => 111011010
[3,3,2,2,2,2] => 110111100 => 101111001 => 110011110
[2,2,2,2,2,2,2] => 111111100 => 111111001 => 011111110
[2,2,2,2,2,2,1,1] => 1111110110 => 1111101101 => 1111110110
[8,5,2] => 10001000100 => 00010001001 => 00100010010
[7,5,2,1] => 10010001010 => 00100010101 => 01000101010
[6,6,3] => 110001000 => 100010001 => 001100010
[6,5,4] => 101010000 => 010100001 => 101000010
[6,5,1,1,1,1] => 101000011110 => 010000111101 => 100001011110
[6,4,2,1,1,1] => 100100101110 => 001001011101 => 010010101110
[6,3,3,1,1,1] => 100011001110 => 000110011101 => 001001101110
[6,3,2,2,1,1] => 100010110110 => 000101101101 => 001010110110
[6,2,2,2,2,1] => 100001111010 => 000011110101 => 000101111010
[5,5,5] => 11100000 => 11000001 => 00001110
[5,5,4,1] => 110100010 => 101000101 => 110001010
[5,5,3,2] => 110010100 => 100101001 => 011010010
[5,4,4,2] => 101100100 => 011001001 => 100110010
[5,4,3,3] => 101011000 => 010110001 => 101000110
[5,4,3,2,1] => 1010101010 => 0101010101 => 1010101010
[4,4,4,3] => 11101000 => 11010001 => 11100010
[4,4,4,2,1] => 111001010 => 110010101 => 011101010
[4,4,3,3,1] => 110110010 => 101100101 => 110011010
[4,4,3,2,2] => 110101100 => 101011001 => 110100110
[4,3,3,3,2] => 101110100 => 011101001 => 101110010
[3,3,3,3,3] => 11111000 => 11110001 => 00111110
[3,3,3,3,2,1] => 111101010 => 111010101 => 111101010
[3,3,3,2,2,2] => 111011100 => 110111001 => 111001110
[8,8] => 1100000000 => 1000000001 => 0000000110
[8,6,2] => 10010000100 => 00100001001 => 01000010010
[8,5,3] => 10001001000 => 00010010001 => 00100100010
[7,5,3,1] => 10010010010 => 00100100101 => 01001001010
[6,6,4] => 110010000 => 100100001 => 011000010
[6,6,3,1] => 1100010010 => 1000100101 => 0011001010
[6,6,2,2] => 1100001100 => 1000011001 => 0001100110
[6,5,5] => 101100000 => 011000001 => 100000110
[6,5,2,1,1,1] => 101000101110 => 010001011101 => 100010101110
[6,4,3,2,1] => 10010101010 => 00101010101 => 01010101010
[6,4,3,1,1,1] => 100101001110 => 001010011101 => 010100101110
[6,4,2,2,1,1] => 100100110110 => 001001101101 => 010010110110
[6,3,3,2,1,1] => 100011010110 => 000110101101 => 001011010110
[6,3,2,2,2,1] => 100010111010 => 000101110101 => 001010111010
[5,5,5,1] => 111000010 => 110000101 => 000111010
[5,5,4,2] => 110100100 => 101001001 => 110010010
[5,5,3,3] => 110011000 => 100110001 => 011000110
[5,5,3,2,1] => 1100101010 => 1001010101 => 0110101010
[5,4,4,3] => 101101000 => 011010001 => 101100010
[5,4,4,2,1] => 1011001010 => 0110010101 => 1001101010
[5,4,3,3,1] => 1010110010 => 0101100101 => 1010011010
[5,4,3,2,2] => 1010101100 => 0101011001 => 1010100110
[4,4,4,4] => 11110000 => 11100001 => 00011110
[4,4,4,3,1] => 111010010 => 110100101 => 111001010
[4,4,4,2,2] => 111001100 => 110011001 => 011100110
[4,4,3,3,2] => 110110100 => 101101001 => 110110010
[4,4,2,2,2,2] => 1100111100 => 1001111001 => 0110011110
[4,3,3,3,3] => 101111000 => 011110001 => 100011110
[3,3,3,3,3,1] => 111110010 => 111100101 => 011111010
[3,3,3,3,2,2] => 111101100 => 111011001 => 111100110
[2,2,2,2,2,2,2,2] => 1111111100 => 1111111001 => 0111111110
[8,6,3] => 10010001000 => 00100010001 => 01000100010
[7,6,3,1] => 10100010010 => 01000100101 => 10001001010
[7,5,4,1] => 10010100010 => 00101000101 => 01010001010
[7,5,3,2] => 10010010100 => 00100101001 => 01001010010
[6,6,5] => 110100000 => 101000001 => 110000010
[6,5,3,2,1] => 10100101010 => 01001010101 => 10010101010
[6,5,3,1,1,1] => 101001001110 => 010010011101 => 100100101110
[6,5,2,2,1,1] => 101000110110 => 010001101101 => 100010110110
[6,4,4,1,1,1] => 100110001110 => 001100011101 => 010001101110
[6,4,3,2,1,1] => 100101010110 => 001010101101 => 010101010110
[6,4,2,2,2,1] => 100100111010 => 001001110101 => 010010111010
[6,3,3,3,1,1] => 100011100110 => 000111001101 => 001001110110
[6,3,3,2,2,1] => 100011011010 => 000110110101 => 001011011010
[5,5,5,2] => 111000100 => 110001001 => 001110010
[5,5,4,3] => 110101000 => 101010001 => 110100010
[5,5,4,2,1] => 1101001010 => 1010010101 => 1100101010
[5,5,3,3,1] => 1100110010 => 1001100101 => 0110011010
[5,5,3,2,2] => 1100101100 => 1001011001 => 0110100110
[5,4,4,4] => 101110000 => 011100001 => 100001110
[5,4,4,3,1] => 1011010010 => 0110100101 => 1011001010
[5,4,4,2,2] => 1011001100 => 0110011001 => 1001100110
[5,4,3,3,2] => 1010110100 => 0101101001 => 1010110010
[4,4,4,4,1] => 111100010 => 111000101 => 001111010
[4,4,4,3,2] => 111010100 => 110101001 => 111010010
[4,4,3,3,3] => 110111000 => 101110001 => 110001110
[3,3,3,3,3,2] => 111110100 => 111101001 => 111110010
[6,5,4,3,2,1] => 101010101010 => 010101010101 => 101010101010
[5,5,4,3,2,1] => 11010101010 => 10101010101 => 11010101010
[6,4,4,3,2,1] => 100110101010 => 001101010101 => 010110101010
[4,4,4,3,2,1] => 1110101010 => 1101010101 => 1110101010
[6,5,3,3,2,1] => 101001101010 => 010011010101 => 100101101010
[6,4,3,3,2,1] => 100101101010 => 001011010101 => 010101101010
[6,3,3,3,2,1] => 100011101010 => 000111010101 => 001011101010
[6,5,4,2,2,1] => 101010011010 => 010100110101 => 101001011010
[6,4,4,2,2,1] => 100110011010 => 001100110101 => 010011011010
[6,5,3,2,2,1] => 101001011010 => 010010110101 => 100101011010
[6,4,3,2,2,1] => 100101011010 => 001010110101 => 010101011010
[6,5,2,2,2,1] => 101000111010 => 010001110101 => 100010111010
[6,5,4,3,1,1] => 101010100110 => 010101001101 => 101010010110
[6,4,4,3,1,1] => 100110100110 => 001101001101 => 010110010110
[6,5,3,3,1,1] => 101001100110 => 010011001101 => 100100110110
[6,4,3,3,1,1] => 100101100110 => 001011001101 => 010100110110
[6,5,4,2,1,1] => 101010010110 => 010100101101 => 101001010110
[6,4,4,2,1,1] => 100110010110 => 001100101101 => 010011010110
[6,5,3,2,1,1] => 101001010110 => 010010101101 => 100101010110
[6,5,4,1,1,1] => 101010001110 => 010100011101 => 101000101110
[6,5,4,3,2] => 10101010100 => 01010101001 => 10101010010
[5,5,4,3,2] => 1101010100 => 1010101001 => 1101010010
[5,4,4,3,2] => 1011010100 => 0110101001 => 1011010010
[5,5,3,3,2] => 1100110100 => 1001101001 => 0110110010
[5,5,4,2,2] => 1101001100 => 1010011001 => 1100100110
[6,5,4,3,1] => 10101010010 => 01010100101 => 10101001010
[5,5,4,3,1] => 1101010010 => 1010100101 => 1101001010
[6,5,4,2,1] => 10101001010 => 01010010101 => 10100101010
[6,6,5,4,3,2] => 110101010100 => 101010101001 => 110101010010
[6,5,5,4,3,2] => 101101010100 => 011010101001 => 101101010010
[6,5,4,4,3,2] => 101011010100 => 010110101001 => 101011010010
[6,5,4,3,3,2] => 101010110100 => 010101101001 => 101010110010
[4,3,3,3,3,2] => 1011110100 => 0111101001 => 1011110010
[6,5,4,3,2,2] => 101010101100 => 010101011001 => 101010100110
[6,6,2,2,2,2] => 110000111100 => 100001111001 => 000110011110
[6,6,5,4,3,1] => 110101010010 => 101010100101 => 110101001010
[6,5,5,4,3,1] => 101101010010 => 011010100101 => 101101001010
[4,4,4,4,3,1] => 1111010010 => 1110100101 => 1111001010
[6,6,5,3,2,1] => 110100101010 => 101001010101 => 110010101010
[6,6,4,3,2,1] => 110010101010 => 100101010101 => 011010101010
[5,4,4,4,3] => 1011101000 => 0111010001 => 1011100010
[5,4,3,3,3] => 1010111000 => 0101110001 => 1010001110
[4,4,4,4,2] => 111100100 => 111001001 => 011110010
[6,5,5,4] => 1011010000 => 0110100001 => 1011000010
[7,6,5,2] => 10101000100 => 01010001001 => 10100010010
[3,3,3,3,3,3] => 111111000 => 111110001 => 001111110
[2,2,2,2,2,2,2,2,2,2] => 111111111100 => 111111111001 => 011111111110
[4,4,4,4,4] => 111110000 => 111100001 => 000111110
[4,4,4,4,4,4] => 1111110000 => 1111100001 => 0001111110
[5,5,5,5] => 111100000 => 111000001 => 000011110
[6,6,6,6] => 1111000000 => 1110000001 => 0000011110
[6,6,6] => 111000000 => 110000001 => 000001110
[10,10] => 110000000000 => 100000000001 => 000000000110
[5,5,5,5,5] => 1111100000 => 1111000001 => 0000111110
[6,5,5,5] => 1011100000 => 0111000001 => 1000001110
[5,4,4,4,4] => 1011110000 => 0111100001 => 1000011110
[5,5,5,5,1] => 1111000010 => 1110000101 => 0001111010
Map
to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.
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.