Identifier
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00135: Binary words —rotate front-to-back⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Images
[1] => 10 => 01 => [2,1]
[2] => 100 => 001 => [3,1]
[1,1] => 110 => 101 => [1,2,1]
[3] => 1000 => 0001 => [4,1]
[2,1] => 1010 => 0101 => [2,2,1]
[1,1,1] => 1110 => 1101 => [1,1,2,1]
[4] => 10000 => 00001 => [5,1]
[3,1] => 10010 => 00101 => [3,2,1]
[2,2] => 1100 => 1001 => [1,3,1]
[2,1,1] => 10110 => 01101 => [2,1,2,1]
[1,1,1,1] => 11110 => 11101 => [1,1,1,2,1]
[5] => 100000 => 000001 => [6,1]
[4,1] => 100010 => 000101 => [4,2,1]
[3,2] => 10100 => 01001 => [2,3,1]
[3,1,1] => 100110 => 001101 => [3,1,2,1]
[2,2,1] => 11010 => 10101 => [1,2,2,1]
[2,1,1,1] => 101110 => 011101 => [2,1,1,2,1]
[1,1,1,1,1] => 111110 => 111101 => [1,1,1,1,2,1]
[6] => 1000000 => 0000001 => [7,1]
[5,1] => 1000010 => 0000101 => [5,2,1]
[4,2] => 100100 => 001001 => [3,3,1]
[4,1,1] => 1000110 => 0001101 => [4,1,2,1]
[3,3] => 11000 => 10001 => [1,4,1]
[3,2,1] => 101010 => 010101 => [2,2,2,1]
[3,1,1,1] => 1001110 => 0011101 => [3,1,1,2,1]
[2,2,2] => 11100 => 11001 => [1,1,3,1]
[2,2,1,1] => 110110 => 101101 => [1,2,1,2,1]
[2,1,1,1,1] => 1011110 => 0111101 => [2,1,1,1,2,1]
[1,1,1,1,1,1] => 1111110 => 1111101 => [1,1,1,1,1,2,1]
[7] => 10000000 => 00000001 => [8,1]
[6,1] => 10000010 => 00000101 => [6,2,1]
[5,2] => 1000100 => 0001001 => [4,3,1]
[5,1,1] => 10000110 => 00001101 => [5,1,2,1]
[4,3] => 101000 => 010001 => [2,4,1]
[4,2,1] => 1001010 => 0010101 => [3,2,2,1]
[4,1,1,1] => 10001110 => 00011101 => [4,1,1,2,1]
[3,3,1] => 110010 => 100101 => [1,3,2,1]
[3,2,2] => 101100 => 011001 => [2,1,3,1]
[3,2,1,1] => 1010110 => 0101101 => [2,2,1,2,1]
[3,1,1,1,1] => 10011110 => 00111101 => [3,1,1,1,2,1]
[2,2,2,1] => 111010 => 110101 => [1,1,2,2,1]
[2,2,1,1,1] => 1101110 => 1011101 => [1,2,1,1,2,1]
[2,1,1,1,1,1] => 10111110 => 01111101 => [2,1,1,1,1,2,1]
[1,1,1,1,1,1,1] => 11111110 => 11111101 => [1,1,1,1,1,1,2,1]
[8] => 100000000 => 000000001 => [9,1]
[7,1] => 100000010 => 000000101 => [7,2,1]
[6,2] => 10000100 => 00001001 => [5,3,1]
[6,1,1] => 100000110 => 000001101 => [6,1,2,1]
[5,3] => 1001000 => 0010001 => [3,4,1]
[5,2,1] => 10001010 => 00010101 => [4,2,2,1]
[5,1,1,1] => 100001110 => 000011101 => [5,1,1,2,1]
[4,4] => 110000 => 100001 => [1,5,1]
[4,3,1] => 1010010 => 0100101 => [2,3,2,1]
[4,2,2] => 1001100 => 0011001 => [3,1,3,1]
[4,2,1,1] => 10010110 => 00101101 => [3,2,1,2,1]
[4,1,1,1,1] => 100011110 => 000111101 => [4,1,1,1,2,1]
[3,3,2] => 110100 => 101001 => [1,2,3,1]
[3,3,1,1] => 1100110 => 1001101 => [1,3,1,2,1]
[3,2,2,1] => 1011010 => 0110101 => [2,1,2,2,1]
[3,2,1,1,1] => 10101110 => 01011101 => [2,2,1,1,2,1]
[3,1,1,1,1,1] => 100111110 => 001111101 => [3,1,1,1,1,2,1]
[2,2,2,2] => 111100 => 111001 => [1,1,1,3,1]
[2,2,2,1,1] => 1110110 => 1101101 => [1,1,2,1,2,1]
[2,2,1,1,1,1] => 11011110 => 10111101 => [1,2,1,1,1,2,1]
[2,1,1,1,1,1,1] => 101111110 => 011111101 => [2,1,1,1,1,1,2,1]
[1,1,1,1,1,1,1,1] => 111111110 => 111111101 => [1,1,1,1,1,1,1,2,1]
[9] => 1000000000 => 0000000001 => [10,1]
[8,1] => 1000000010 => 0000000101 => [8,2,1]
[7,2] => 100000100 => 000001001 => [6,3,1]
[7,1,1] => 1000000110 => 0000001101 => [7,1,2,1]
[6,3] => 10001000 => 00010001 => [4,4,1]
[6,2,1] => 100001010 => 000010101 => [5,2,2,1]
[6,1,1,1] => 1000001110 => 0000011101 => [6,1,1,2,1]
[5,4] => 1010000 => 0100001 => [2,5,1]
[5,3,1] => 10010010 => 00100101 => [3,3,2,1]
[5,2,2] => 10001100 => 00011001 => [4,1,3,1]
[5,2,1,1] => 100010110 => 000101101 => [4,2,1,2,1]
[5,1,1,1,1] => 1000011110 => 0000111101 => [5,1,1,1,2,1]
[4,4,1] => 1100010 => 1000101 => [1,4,2,1]
[4,3,2] => 1010100 => 0101001 => [2,2,3,1]
[4,3,1,1] => 10100110 => 01001101 => [2,3,1,2,1]
[4,2,2,1] => 10011010 => 00110101 => [3,1,2,2,1]
[4,2,1,1,1] => 100101110 => 001011101 => [3,2,1,1,2,1]
[4,1,1,1,1,1] => 1000111110 => 0001111101 => [4,1,1,1,1,2,1]
[3,3,3] => 111000 => 110001 => [1,1,4,1]
[3,3,2,1] => 1101010 => 1010101 => [1,2,2,2,1]
[3,3,1,1,1] => 11001110 => 10011101 => [1,3,1,1,2,1]
[3,2,2,2] => 1011100 => 0111001 => [2,1,1,3,1]
[3,2,2,1,1] => 10110110 => 01101101 => [2,1,2,1,2,1]
[3,2,1,1,1,1] => 101011110 => 010111101 => [2,2,1,1,1,2,1]
[3,1,1,1,1,1,1] => 1001111110 => 0011111101 => [3,1,1,1,1,1,2,1]
[2,2,2,2,1] => 1111010 => 1110101 => [1,1,1,2,2,1]
[2,2,2,1,1,1] => 11101110 => 11011101 => [1,1,2,1,1,2,1]
[2,2,1,1,1,1,1] => 110111110 => 101111101 => [1,2,1,1,1,1,2,1]
[2,1,1,1,1,1,1,1] => 1011111110 => 0111111101 => [2,1,1,1,1,1,1,2,1]
[1,1,1,1,1,1,1,1,1] => 1111111110 => 1111111101 => [1,1,1,1,1,1,1,1,2,1]
[10] => 10000000000 => 00000000001 => [11,1]
[9,1] => 10000000010 => 00000000101 => [9,2,1]
[8,2] => 1000000100 => 0000001001 => [7,3,1]
[8,1,1] => 10000000110 => 00000001101 => [8,1,2,1]
[7,3] => 100001000 => 000010001 => [5,4,1]
>>> Load all 482 entries. <<<
[7,2,1] => 1000001010 => 0000010101 => [6,2,2,1]
[7,1,1,1] => 10000001110 => 00000011101 => [7,1,1,2,1]
[6,4] => 10010000 => 00100001 => [3,5,1]
[6,3,1] => 100010010 => 000100101 => [4,3,2,1]
[6,2,2] => 100001100 => 000011001 => [5,1,3,1]
[6,2,1,1] => 1000010110 => 0000101101 => [5,2,1,2,1]
[6,1,1,1,1] => 10000011110 => 00000111101 => [6,1,1,1,2,1]
[5,5] => 1100000 => 1000001 => [1,6,1]
[5,4,1] => 10100010 => 01000101 => [2,4,2,1]
[5,3,2] => 10010100 => 00101001 => [3,2,3,1]
[5,3,1,1] => 100100110 => 001001101 => [3,3,1,2,1]
[5,2,2,1] => 100011010 => 000110101 => [4,1,2,2,1]
[5,2,1,1,1] => 1000101110 => 0001011101 => [4,2,1,1,2,1]
[5,1,1,1,1,1] => 10000111110 => 00001111101 => [5,1,1,1,1,2,1]
[4,4,2] => 1100100 => 1001001 => [1,3,3,1]
[4,4,1,1] => 11000110 => 10001101 => [1,4,1,2,1]
[4,3,3] => 1011000 => 0110001 => [2,1,4,1]
[4,3,2,1] => 10101010 => 01010101 => [2,2,2,2,1]
[4,3,1,1,1] => 101001110 => 010011101 => [2,3,1,1,2,1]
[4,2,2,2] => 10011100 => 00111001 => [3,1,1,3,1]
[4,2,2,1,1] => 100110110 => 001101101 => [3,1,2,1,2,1]
[4,2,1,1,1,1] => 1001011110 => 0010111101 => [3,2,1,1,1,2,1]
[4,1,1,1,1,1,1] => 10001111110 => 00011111101 => [4,1,1,1,1,1,2,1]
[3,3,3,1] => 1110010 => 1100101 => [1,1,3,2,1]
[3,3,2,2] => 1101100 => 1011001 => [1,2,1,3,1]
[3,3,2,1,1] => 11010110 => 10101101 => [1,2,2,1,2,1]
[3,3,1,1,1,1] => 110011110 => 100111101 => [1,3,1,1,1,2,1]
[3,2,2,2,1] => 10111010 => 01110101 => [2,1,1,2,2,1]
[3,2,2,1,1,1] => 101101110 => 011011101 => [2,1,2,1,1,2,1]
[3,2,1,1,1,1,1] => 1010111110 => 0101111101 => [2,2,1,1,1,1,2,1]
[3,1,1,1,1,1,1,1] => 10011111110 => 00111111101 => [3,1,1,1,1,1,1,2,1]
[2,2,2,2,2] => 1111100 => 1111001 => [1,1,1,1,3,1]
[2,2,2,2,1,1] => 11110110 => 11101101 => [1,1,1,2,1,2,1]
[2,2,2,1,1,1,1] => 111011110 => 110111101 => [1,1,2,1,1,1,2,1]
[2,2,1,1,1,1,1,1] => 1101111110 => 1011111101 => [1,2,1,1,1,1,1,2,1]
[2,1,1,1,1,1,1,1,1] => 10111111110 => 01111111101 => [2,1,1,1,1,1,1,1,2,1]
[1,1,1,1,1,1,1,1,1,1] => 11111111110 => 11111111101 => [1,1,1,1,1,1,1,1,1,2,1]
[9,2] => 10000000100 => 00000001001 => [8,3,1]
[8,2,1] => 10000001010 => 00000010101 => [7,2,2,1]
[7,4] => 100010000 => 000100001 => [4,5,1]
[7,2,1,1] => 10000010110 => 00000101101 => [6,2,1,2,1]
[6,5] => 10100000 => 01000001 => [2,6,1]
[6,4,1] => 100100010 => 001000101 => [3,4,2,1]
[6,3,2] => 100010100 => 000101001 => [4,2,3,1]
[6,2,1,1,1] => 10000101110 => 00001011101 => [5,2,1,1,2,1]
[6,1,1,1,1,1] => 100000111110 => 000001111101 => [6,1,1,1,1,2,1]
[5,5,1] => 11000010 => 10000101 => [1,5,2,1]
[5,4,2] => 10100100 => 01001001 => [2,3,3,1]
[5,4,1,1] => 101000110 => 010001101 => [2,4,1,2,1]
[5,3,3] => 10011000 => 00110001 => [3,1,4,1]
[5,3,2,1] => 100101010 => 001010101 => [3,2,2,2,1]
[5,3,1,1,1] => 1001001110 => 0010011101 => [3,3,1,1,2,1]
[5,2,2,2] => 100011100 => 000111001 => [4,1,1,3,1]
[5,2,2,1,1] => 1000110110 => 0001101101 => [4,1,2,1,2,1]
[5,2,1,1,1,1] => 10001011110 => 00010111101 => [4,2,1,1,1,2,1]
[4,4,3] => 1101000 => 1010001 => [1,2,4,1]
[4,4,2,1] => 11001010 => 10010101 => [1,3,2,2,1]
[4,4,1,1,1] => 110001110 => 100011101 => [1,4,1,1,2,1]
[4,3,3,1] => 10110010 => 01100101 => [2,1,3,2,1]
[4,3,2,2] => 10101100 => 01011001 => [2,2,1,3,1]
[4,3,2,1,1] => 101010110 => 010101101 => [2,2,2,1,2,1]
[4,2,2,2,1] => 100111010 => 001110101 => [3,1,1,2,2,1]
[4,2,1,1,1,1,1] => 10010111110 => 00101111101 => [3,2,1,1,1,1,2,1]
[3,3,3,2] => 1110100 => 1101001 => [1,1,2,3,1]
[3,3,3,1,1] => 11100110 => 11001101 => [1,1,3,1,2,1]
[3,3,2,2,1] => 11011010 => 10110101 => [1,2,1,2,2,1]
[3,3,2,1,1,1] => 110101110 => 101011101 => [1,2,2,1,1,2,1]
[3,2,2,2,2] => 10111100 => 01111001 => [2,1,1,1,3,1]
[3,2,2,2,1,1] => 101110110 => 011101101 => [2,1,1,2,1,2,1]
[3,2,1,1,1,1,1,1] => 10101111110 => 01011111101 => [2,2,1,1,1,1,1,2,1]
[2,2,2,2,2,1] => 11111010 => 11110101 => [1,1,1,1,2,2,1]
[2,2,2,2,1,1,1] => 111101110 => 111011101 => [1,1,1,2,1,1,2,1]
[2,2,2,1,1,1,1,1] => 1110111110 => 1101111101 => [1,1,2,1,1,1,1,2,1]
[2,2,1,1,1,1,1,1,1] => 11011111110 => 10111111101 => [1,2,1,1,1,1,1,1,2,1]
[10,2] => 100000000100 => 000000001001 => [9,3,1]
[8,4] => 1000010000 => 0000100001 => [5,5,1]
[7,5] => 100100000 => 001000001 => [3,6,1]
[6,6] => 11000000 => 10000001 => [1,7,1]
[6,5,1] => 101000010 => 010000101 => [2,5,2,1]
[6,4,2] => 100100100 => 001001001 => [3,3,3,1]
[6,4,1,1] => 1001000110 => 0010001101 => [3,4,1,2,1]
[6,3,3] => 100011000 => 000110001 => [4,1,4,1]
[6,3,2,1] => 1000101010 => 0001010101 => [4,2,2,2,1]
[6,2,2,2] => 1000011100 => 0000111001 => [5,1,1,3,1]
[6,2,1,1,1,1] => 100001011110 => 000010111101 => [5,2,1,1,1,2,1]
[5,5,2] => 11000100 => 10001001 => [1,4,3,1]
[5,5,1,1] => 110000110 => 100001101 => [1,5,1,2,1]
[5,4,3] => 10101000 => 01010001 => [2,2,4,1]
[5,4,2,1] => 101001010 => 010010101 => [2,3,2,2,1]
[5,4,1,1,1] => 1010001110 => 0100011101 => [2,4,1,1,2,1]
[5,3,3,1] => 100110010 => 001100101 => [3,1,3,2,1]
[5,3,2,2] => 100101100 => 001011001 => [3,2,1,3,1]
[5,3,2,1,1] => 1001010110 => 0010101101 => [3,2,2,1,2,1]
[5,2,2,2,1] => 1000111010 => 0001110101 => [4,1,1,2,2,1]
[4,4,4] => 1110000 => 1100001 => [1,1,5,1]
[4,4,3,1] => 11010010 => 10100101 => [1,2,3,2,1]
[4,4,2,2] => 11001100 => 10011001 => [1,3,1,3,1]
[4,4,2,1,1] => 110010110 => 100101101 => [1,3,2,1,2,1]
[4,4,1,1,1,1] => 1100011110 => 1000111101 => [1,4,1,1,1,2,1]
[4,3,3,2] => 10110100 => 01101001 => [2,1,2,3,1]
[4,3,3,1,1] => 101100110 => 011001101 => [2,1,3,1,2,1]
[4,3,2,2,1] => 101011010 => 010110101 => [2,2,1,2,2,1]
[4,2,2,2,2] => 100111100 => 001111001 => [3,1,1,1,3,1]
[3,3,3,3] => 1111000 => 1110001 => [1,1,1,4,1]
[3,3,3,2,1] => 11101010 => 11010101 => [1,1,2,2,2,1]
[3,3,3,1,1,1] => 111001110 => 110011101 => [1,1,3,1,1,2,1]
[3,3,2,2,2] => 11011100 => 10111001 => [1,2,1,1,3,1]
[3,3,2,2,1,1] => 110110110 => 101101101 => [1,2,1,2,1,2,1]
[3,2,2,2,2,1] => 101111010 => 011110101 => [2,1,1,1,2,2,1]
[2,2,2,2,2,2] => 11111100 => 11111001 => [1,1,1,1,1,3,1]
[2,2,2,2,2,1,1] => 111110110 => 111101101 => [1,1,1,1,2,1,2,1]
[7,6] => 101000000 => 010000001 => [2,7,1]
[6,6,1] => 110000010 => 100000101 => [1,6,2,1]
[6,5,2] => 101000100 => 010001001 => [2,4,3,1]
[6,4,3] => 100101000 => 001010001 => [3,2,4,1]
[6,4,2,1] => 1001001010 => 0010010101 => [3,3,2,2,1]
[6,3,1,1,1,1] => 100010011110 => 000100111101 => [4,3,1,1,1,2,1]
[6,2,2,1,1,1] => 100001101110 => 000011011101 => [5,1,2,1,1,2,1]
[5,5,3] => 11001000 => 10010001 => [1,3,4,1]
[5,5,2,1] => 110001010 => 100010101 => [1,4,2,2,1]
[5,4,4] => 10110000 => 01100001 => [2,1,5,1]
[5,4,3,1] => 101010010 => 010100101 => [2,2,3,2,1]
[5,4,2,2] => 101001100 => 010011001 => [2,3,1,3,1]
[5,4,2,1,1] => 1010010110 => 0100101101 => [2,3,2,1,2,1]
[5,3,3,2] => 100110100 => 001101001 => [3,1,2,3,1]
[5,3,3,1,1] => 1001100110 => 0011001101 => [3,1,3,1,2,1]
[5,3,2,2,1] => 1001011010 => 0010110101 => [3,2,1,2,2,1]
[5,2,2,2,2] => 1000111100 => 0001111001 => [4,1,1,1,3,1]
[4,4,4,1] => 11100010 => 11000101 => [1,1,4,2,1]
[4,4,3,2] => 11010100 => 10101001 => [1,2,2,3,1]
[4,4,3,1,1] => 110100110 => 101001101 => [1,2,3,1,2,1]
[4,4,2,2,1] => 110011010 => 100110101 => [1,3,1,2,2,1]
[4,4,2,1,1,1] => 1100101110 => 1001011101 => [1,3,2,1,1,2,1]
[4,3,3,3] => 10111000 => 01110001 => [2,1,1,4,1]
[4,3,3,2,1] => 101101010 => 011010101 => [2,1,2,2,2,1]
[4,3,2,2,2] => 101011100 => 010111001 => [2,2,1,1,3,1]
[3,3,3,3,1] => 11110010 => 11100101 => [1,1,1,3,2,1]
[3,3,3,2,2] => 11101100 => 11011001 => [1,1,2,1,3,1]
[3,3,3,2,1,1] => 111010110 => 110101101 => [1,1,2,2,1,2,1]
[3,3,2,2,2,1] => 110111010 => 101110101 => [1,2,1,1,2,2,1]
[3,2,2,2,2,2] => 101111100 => 011111001 => [2,1,1,1,1,3,1]
[3,2,2,2,1,1,1,1] => 10111011110 => 01110111101 => [2,1,1,2,1,1,1,2,1]
[2,2,2,2,2,2,1] => 111111010 => 111110101 => [1,1,1,1,1,2,2,1]
[2,2,2,2,2,1,1,1] => 1111101110 => 1111011101 => [1,1,1,1,2,1,1,2,1]
[2,2,2,2,1,1,1,1,1] => 11110111110 => 11101111101 => [1,1,1,2,1,1,1,1,2,1]
[10,4] => 100000010000 => 000000100001 => [7,5,1]
[8,6] => 1001000000 => 0010000001 => [3,7,1]
[8,5,1] => 10001000010 => 00010000101 => [4,5,2,1]
[8,2,2,2] => 100000011100 => 000000111001 => [7,1,1,3,1]
[7,7] => 110000000 => 100000001 => [1,8,1]
[7,6,1] => 1010000010 => 0100000101 => [2,6,2,1]
[7,4,2,1] => 10001001010 => 00010010101 => [4,3,2,2,1]
[6,6,2] => 110000100 => 100001001 => [1,5,3,1]
[6,6,1,1] => 1100000110 => 1000001101 => [1,6,1,2,1]
[6,5,3] => 101001000 => 010010001 => [2,3,4,1]
[6,5,2,1] => 1010001010 => 0100010101 => [2,4,2,2,1]
[6,4,4] => 100110000 => 001100001 => [3,1,5,1]
[6,4,3,1] => 1001010010 => 0010100101 => [3,2,3,2,1]
[6,4,2,2] => 1001001100 => 0010011001 => [3,3,1,3,1]
[6,4,1,1,1,1] => 100100011110 => 001000111101 => [3,4,1,1,1,2,1]
[6,3,3,2] => 1000110100 => 0001101001 => [4,1,2,3,1]
[6,3,2,1,1,1] => 100010101110 => 000101011101 => [4,2,2,1,1,2,1]
[6,2,2,2,1,1] => 100001110110 => 000011101101 => [5,1,1,2,1,2,1]
[5,5,4] => 11010000 => 10100001 => [1,2,5,1]
[5,5,3,1] => 110010010 => 100100101 => [1,3,3,2,1]
[5,5,2,2] => 110001100 => 100011001 => [1,4,1,3,1]
[5,4,4,1] => 101100010 => 011000101 => [2,1,4,2,1]
[5,4,3,2] => 101010100 => 010101001 => [2,2,2,3,1]
[5,4,3,1,1] => 1010100110 => 0101001101 => [2,2,3,1,2,1]
[5,4,2,2,1] => 1010011010 => 0100110101 => [2,3,1,2,2,1]
[5,3,3,3] => 100111000 => 001110001 => [3,1,1,4,1]
[5,3,3,2,1] => 1001101010 => 0011010101 => [3,1,2,2,2,1]
[4,4,4,2] => 11100100 => 11001001 => [1,1,3,3,1]
[4,4,4,1,1] => 111000110 => 110001101 => [1,1,4,1,2,1]
[4,4,3,3] => 11011000 => 10110001 => [1,2,1,4,1]
[4,4,3,2,1] => 110101010 => 101010101 => [1,2,2,2,2,1]
[4,4,3,1,1,1] => 1101001110 => 1010011101 => [1,2,3,1,1,2,1]
[4,4,2,2,2] => 110011100 => 100111001 => [1,3,1,1,3,1]
[4,3,3,3,1] => 101110010 => 011100101 => [2,1,1,3,2,1]
[4,3,3,2,2] => 101101100 => 011011001 => [2,1,2,1,3,1]
[4,3,2,2,1,1,1] => 10101101110 => 01011011101 => [2,2,1,2,1,1,2,1]
[4,2,2,2,2,2] => 1001111100 => 0011111001 => [3,1,1,1,1,3,1]
[3,3,3,3,2] => 11110100 => 11101001 => [1,1,1,2,3,1]
[3,3,3,3,1,1] => 111100110 => 111001101 => [1,1,1,3,1,2,1]
[3,3,3,2,2,1] => 111011010 => 110110101 => [1,1,2,1,2,2,1]
[3,3,2,2,2,2] => 110111100 => 101111001 => [1,2,1,1,1,3,1]
[3,3,2,2,1,1,1,1] => 11011011110 => 10110111101 => [1,2,1,2,1,1,1,2,1]
[3,2,2,2,2,1,1,1] => 10111101110 => 01111011101 => [2,1,1,1,2,1,1,2,1]
[2,2,2,2,2,2,2] => 111111100 => 111111001 => [1,1,1,1,1,1,3,1]
[2,2,2,2,2,2,1,1] => 1111110110 => 1111101101 => [1,1,1,1,1,2,1,2,1]
[8,5,2] => 10001000100 => 00010001001 => [4,4,3,1]
[7,7,1] => 1100000010 => 1000000101 => [1,7,2,1]
[7,5,2,1] => 10010001010 => 00100010101 => [3,4,2,2,1]
[7,4,3,1] => 10001010010 => 00010100101 => [4,2,3,2,1]
[6,6,3] => 110001000 => 100010001 => [1,4,4,1]
[6,6,2,1] => 1100001010 => 1000010101 => [1,5,2,2,1]
[6,5,4] => 101010000 => 010100001 => [2,2,5,1]
[6,5,2,2] => 1010001100 => 0100011001 => [2,4,1,3,1]
[6,5,1,1,1,1] => 101000011110 => 010000111101 => [2,5,1,1,1,2,1]
[6,4,2,1,1,1] => 100100101110 => 001001011101 => [3,3,2,1,1,2,1]
[6,3,3,1,1,1] => 100011001110 => 000110011101 => [4,1,3,1,1,2,1]
[6,3,2,2,1,1] => 100010110110 => 000101101101 => [4,2,1,2,1,2,1]
[6,2,2,2,2,1] => 100001111010 => 000011110101 => [5,1,1,1,2,2,1]
[5,5,5] => 11100000 => 11000001 => [1,1,6,1]
[5,5,4,1] => 110100010 => 101000101 => [1,2,4,2,1]
[5,5,3,2] => 110010100 => 100101001 => [1,3,2,3,1]
[5,5,3,1,1] => 1100100110 => 1001001101 => [1,3,3,1,2,1]
[5,4,4,2] => 101100100 => 011001001 => [2,1,3,3,1]
[5,4,3,3] => 101011000 => 010110001 => [2,2,1,4,1]
[5,4,3,2,1] => 1010101010 => 0101010101 => [2,2,2,2,2,1]
[5,3,3,2,2] => 1001101100 => 0011011001 => [3,1,2,1,3,1]
[4,4,4,3] => 11101000 => 11010001 => [1,1,2,4,1]
[4,4,4,2,1] => 111001010 => 110010101 => [1,1,3,2,2,1]
[4,4,3,3,1] => 110110010 => 101100101 => [1,2,1,3,2,1]
[4,4,3,2,2] => 110101100 => 101011001 => [1,2,2,1,3,1]
[4,3,3,3,2] => 101110100 => 011101001 => [2,1,1,2,3,1]
[4,3,3,2,1,1,1] => 10110101110 => 01101011101 => [2,1,2,2,1,1,2,1]
[4,3,2,2,2,1,1] => 10101110110 => 01011101101 => [2,2,1,1,2,1,2,1]
[3,3,3,3,3] => 11111000 => 11110001 => [1,1,1,1,4,1]
[3,3,3,3,2,1] => 111101010 => 111010101 => [1,1,1,2,2,2,1]
[3,3,3,2,2,2] => 111011100 => 110111001 => [1,1,2,1,1,3,1]
[3,3,3,2,1,1,1,1] => 11101011110 => 11010111101 => [1,1,2,2,1,1,1,2,1]
[3,3,2,2,2,1,1,1] => 11011101110 => 10111011101 => [1,2,1,1,2,1,1,2,1]
[2,2,2,2,2,2,2,1] => 1111111010 => 1111110101 => [1,1,1,1,1,1,2,2,1]
[10,6] => 100001000000 => 000010000001 => [5,7,1]
[8,8] => 1100000000 => 1000000001 => [1,9,1]
[8,6,2] => 10010000100 => 00100001001 => [3,5,3,1]
[8,5,3] => 10001001000 => 00010010001 => [4,3,4,1]
[8,4,2,2] => 100001001100 => 000010011001 => [5,3,1,3,1]
[8,3,3,2] => 100000110100 => 000001101001 => [6,1,2,3,1]
[7,5,3,1] => 10010010010 => 00100100101 => [3,3,3,2,1]
[7,4,3,2] => 10001010100 => 00010101001 => [4,2,2,3,1]
[6,6,4] => 110010000 => 100100001 => [1,3,5,1]
[6,6,3,1] => 1100010010 => 1000100101 => [1,4,3,2,1]
[6,6,2,2] => 1100001100 => 1000011001 => [1,5,1,3,1]
[6,5,5] => 101100000 => 011000001 => [2,1,6,1]
[6,5,4,1] => 1010100010 => 0101000101 => [2,2,4,2,1]
[6,5,3,2] => 1010010100 => 0100101001 => [2,3,2,3,1]
[6,5,2,1,1,1] => 101000101110 => 010001011101 => [2,4,2,1,1,2,1]
[6,4,4,2] => 1001100100 => 0011001001 => [3,1,3,3,1]
[6,4,3,3] => 1001011000 => 0010110001 => [3,2,1,4,1]
[6,4,3,2,1] => 10010101010 => 00101010101 => [3,2,2,2,2,1]
[6,4,3,1,1,1] => 100101001110 => 001010011101 => [3,2,3,1,1,2,1]
[6,4,2,2,1,1] => 100100110110 => 001001101101 => [3,3,1,2,1,2,1]
[6,3,3,2,1,1] => 100011010110 => 000110101101 => [4,1,2,2,1,2,1]
[6,3,2,2,2,1] => 100010111010 => 000101110101 => [4,2,1,1,2,2,1]
[6,2,2,2,2,2] => 100001111100 => 000011111001 => [5,1,1,1,1,3,1]
[5,5,5,1] => 111000010 => 110000101 => [1,1,5,2,1]
[5,5,4,2] => 110100100 => 101001001 => [1,2,3,3,1]
[5,5,3,3] => 110011000 => 100110001 => [1,3,1,4,1]
[5,5,3,2,1] => 1100101010 => 1001010101 => [1,3,2,2,2,1]
[5,5,2,2,2] => 1100011100 => 1000111001 => [1,4,1,1,3,1]
[5,4,4,3] => 101101000 => 011010001 => [2,1,2,4,1]
[5,4,4,2,1] => 1011001010 => 0110010101 => [2,1,3,2,2,1]
[5,4,3,3,1] => 1010110010 => 0101100101 => [2,2,1,3,2,1]
[5,4,3,2,2] => 1010101100 => 0101011001 => [2,2,2,1,3,1]
[5,4,3,2,1,1] => 10101010110 => 01010101101 => [2,2,2,2,1,2,1]
[4,4,4,4] => 11110000 => 11100001 => [1,1,1,5,1]
[4,4,4,3,1] => 111010010 => 110100101 => [1,1,2,3,2,1]
[4,4,4,2,2] => 111001100 => 110011001 => [1,1,3,1,3,1]
[4,4,4,2,1,1] => 1110010110 => 1100101101 => [1,1,3,2,1,2,1]
[4,4,3,3,2] => 110110100 => 101101001 => [1,2,1,2,3,1]
[4,4,3,2,1,1,1] => 11010101110 => 10101011101 => [1,2,2,2,1,1,2,1]
[4,4,2,2,2,2] => 1100111100 => 1001111001 => [1,3,1,1,1,3,1]
[4,3,3,3,3] => 101111000 => 011110001 => [2,1,1,1,4,1]
[4,3,3,2,2,2] => 1011011100 => 0110111001 => [2,1,2,1,1,3,1]
[4,3,3,2,2,1,1] => 10110110110 => 01101101101 => [2,1,2,1,2,1,2,1]
[3,3,3,3,3,1] => 111110010 => 111100101 => [1,1,1,1,3,2,1]
[3,3,3,3,2,2] => 111101100 => 111011001 => [1,1,1,2,1,3,1]
[3,3,3,2,2,1,1,1] => 11101101110 => 11011011101 => [1,1,2,1,2,1,1,2,1]
[3,3,2,2,2,2,1,1] => 11011110110 => 10111101101 => [1,2,1,1,1,2,1,2,1]
[2,2,2,2,2,2,2,2] => 1111111100 => 1111111001 => [1,1,1,1,1,1,1,3,1]
[8,8,1] => 11000000010 => 10000000101 => [1,8,2,1]
[8,6,3] => 10010001000 => 00100010001 => [3,4,4,1]
[7,6,3,1] => 10100010010 => 01000100101 => [2,4,3,2,1]
[7,5,4,1] => 10010100010 => 00101000101 => [3,2,4,2,1]
[7,5,3,2] => 10010010100 => 00100101001 => [3,3,2,3,1]
[6,6,5] => 110100000 => 101000001 => [1,2,6,1]
[6,5,3,3] => 1010011000 => 0100110001 => [2,3,1,4,1]
[6,5,3,2,1] => 10100101010 => 01001010101 => [2,3,2,2,2,1]
[6,5,3,1,1,1] => 101001001110 => 010010011101 => [2,3,3,1,1,2,1]
[6,5,2,2,1,1] => 101000110110 => 010001101101 => [2,4,1,2,1,2,1]
[6,4,4,1,1,1] => 100110001110 => 001100011101 => [3,1,4,1,1,2,1]
[6,4,3,2,1,1] => 100101010110 => 001010101101 => [3,2,2,2,1,2,1]
[6,4,2,2,2,1] => 100100111010 => 001001110101 => [3,3,1,1,2,2,1]
[6,3,3,3,1,1] => 100011100110 => 000111001101 => [4,1,1,3,1,2,1]
[6,3,3,2,2,1] => 100011011010 => 000110110101 => [4,1,2,1,2,2,1]
[5,5,5,2] => 111000100 => 110001001 => [1,1,4,3,1]
[5,5,4,3] => 110101000 => 101010001 => [1,2,2,4,1]
[5,5,4,2,1] => 1101001010 => 1010010101 => [1,2,3,2,2,1]
[5,5,3,3,1] => 1100110010 => 1001100101 => [1,3,1,3,2,1]
[5,5,3,2,2] => 1100101100 => 1001011001 => [1,3,2,1,3,1]
[5,4,4,4] => 101110000 => 011100001 => [2,1,1,5,1]
[5,4,4,3,1] => 1011010010 => 0110100101 => [2,1,2,3,2,1]
[5,4,4,2,2] => 1011001100 => 0110011001 => [2,1,3,1,3,1]
[5,4,3,3,2] => 1010110100 => 0101101001 => [2,2,1,2,3,1]
[5,4,3,2,2,1] => 10101011010 => 01010110101 => [2,2,2,1,2,2,1]
[5,3,3,3,3] => 1001111000 => 0011110001 => [3,1,1,1,4,1]
[4,4,4,4,1] => 111100010 => 111000101 => [1,1,1,4,2,1]
[4,4,4,3,2] => 111010100 => 110101001 => [1,1,2,2,3,1]
[4,4,3,3,3] => 110111000 => 101110001 => [1,2,1,1,4,1]
[4,4,3,2,2,1,1] => 11010110110 => 10101101101 => [1,2,2,1,2,1,2,1]
[4,3,3,3,2,1,1] => 10111010110 => 01110101101 => [2,1,1,2,2,1,2,1]
[4,3,3,2,2,2,1] => 10110111010 => 01101110101 => [2,1,2,1,1,2,2,1]
[3,3,3,3,3,2] => 111110100 => 111101001 => [1,1,1,1,2,3,1]
[3,3,3,2,2,2,1,1] => 11101110110 => 11011101101 => [1,1,2,1,1,2,1,2,1]
[6,5,4,3,2,1] => 101010101010 => 010101010101 => [2,2,2,2,2,2,1]
[5,5,4,3,2,1] => 11010101010 => 10101010101 => [1,2,2,2,2,2,1]
[6,4,4,3,2,1] => 100110101010 => 001101010101 => [3,1,2,2,2,2,1]
[5,4,4,3,2,1] => 10110101010 => 01101010101 => [2,1,2,2,2,2,1]
[4,4,4,3,2,1] => 1110101010 => 1101010101 => [1,1,2,2,2,2,1]
[6,5,3,3,2,1] => 101001101010 => 010011010101 => [2,3,1,2,2,2,1]
[6,4,3,3,2,1] => 100101101010 => 001011010101 => [3,2,1,2,2,2,1]
[5,4,3,3,2,1] => 10101101010 => 01011010101 => [2,2,1,2,2,2,1]
[6,3,3,3,2,1] => 100011101010 => 000111010101 => [4,1,1,2,2,2,1]
[6,5,4,2,2,1] => 101010011010 => 010100110101 => [2,2,3,1,2,2,1]
[6,4,4,2,2,1] => 100110011010 => 001100110101 => [3,1,3,1,2,2,1]
[6,5,3,2,2,1] => 101001011010 => 010010110101 => [2,3,2,1,2,2,1]
[6,4,3,2,2,1] => 100101011010 => 001010110101 => [3,2,2,1,2,2,1]
[6,5,2,2,2,1] => 101000111010 => 010001110101 => [2,4,1,1,2,2,1]
[6,5,4,3,1,1] => 101010100110 => 010101001101 => [2,2,2,3,1,2,1]
[6,4,4,3,1,1] => 100110100110 => 001101001101 => [3,1,2,3,1,2,1]
[6,5,3,3,1,1] => 101001100110 => 010011001101 => [2,3,1,3,1,2,1]
[6,4,3,3,1,1] => 100101100110 => 001011001101 => [3,2,1,3,1,2,1]
[6,5,4,2,1,1] => 101010010110 => 010100101101 => [2,2,3,2,1,2,1]
[6,4,4,2,1,1] => 100110010110 => 001100101101 => [3,1,3,2,1,2,1]
[6,5,3,2,1,1] => 101001010110 => 010010101101 => [2,3,2,2,1,2,1]
[6,5,4,1,1,1] => 101010001110 => 010100011101 => [2,2,4,1,1,2,1]
[6,5,4,3,2] => 10101010100 => 01010101001 => [2,2,2,2,3,1]
[5,5,4,3,2] => 1101010100 => 1010101001 => [1,2,2,2,3,1]
[5,4,4,3,2] => 1011010100 => 0110101001 => [2,1,2,2,3,1]
[5,5,3,3,2] => 1100110100 => 1001101001 => [1,3,1,2,3,1]
[5,5,4,2,2] => 1101001100 => 1010011001 => [1,2,3,1,3,1]
[6,5,4,3,1] => 10101010010 => 01010100101 => [2,2,2,3,2,1]
[5,5,4,3,1] => 1101010010 => 1010100101 => [1,2,2,3,2,1]
[6,5,4,2,1] => 10101001010 => 01010010101 => [2,2,3,2,2,1]
[6,5,4,3] => 1010101000 => 0101010001 => [2,2,2,4,1]
[7,6,5,4,3,2,1] => 10101010101010 => 01010101010101 => [2,2,2,2,2,2,2,1]
[3,3,3,3,3,2,1] => 1111101010 => 1111010101 => [1,1,1,1,2,2,2,1]
[6,6,5,4,3,2] => 110101010100 => 101010101001 => [1,2,2,2,2,3,1]
[6,5,5,4,3,2] => 101101010100 => 011010101001 => [2,1,2,2,2,3,1]
[5,5,5,4,3,2] => 11101010100 => 11010101001 => [1,1,2,2,2,3,1]
[6,5,4,4,3,2] => 101011010100 => 010110101001 => [2,2,1,2,2,3,1]
[6,5,4,3,3,2] => 101010110100 => 010101101001 => [2,2,2,1,2,3,1]
[4,3,3,3,3,2] => 1011110100 => 0111101001 => [2,1,1,1,2,3,1]
[6,5,4,3,2,2] => 101010101100 => 010101011001 => [2,2,2,2,1,3,1]
[4,4,4,3,2,2] => 1110101100 => 1101011001 => [1,1,2,2,1,3,1]
[6,6,2,2,2,2] => 110000111100 => 100001111001 => [1,5,1,1,1,3,1]
[6,6,5,4,3,1] => 110101010010 => 101010100101 => [1,2,2,2,3,2,1]
[6,5,5,4,3,1] => 101101010010 => 011010100101 => [2,1,2,2,3,2,1]
[4,4,4,4,3,1] => 1111010010 => 1110100101 => [1,1,1,2,3,2,1]
[4,4,4,4,2,1] => 1111001010 => 1110010101 => [1,1,1,3,2,2,1]
[6,6,5,3,2,1] => 110100101010 => 101001010101 => [1,2,3,2,2,2,1]
[6,6,4,3,2,1] => 110010101010 => 100101010101 => [1,3,2,2,2,2,1]
[6,6,5,4,3] => 11010101000 => 10101010001 => [1,2,2,2,4,1]
[5,4,4,4,3] => 1011101000 => 0111010001 => [2,1,1,2,4,1]
[5,4,3,3,3] => 1010111000 => 0101110001 => [2,2,1,1,4,1]
[4,4,4,4,2] => 111100100 => 111001001 => [1,1,1,3,3,1]
[6,5,5,4] => 1011010000 => 0110100001 => [2,1,2,5,1]
[7,6,5,2] => 10101000100 => 01010001001 => [2,2,4,3,1]
[3,3,3,3,3,3] => 111111000 => 111110001 => [1,1,1,1,1,4,1]
[3,3,3,3,3,3,3,3] => 11111111000 => 11111110001 => [1,1,1,1,1,1,1,4,1]
[2,2,2,2,2,2,2,2,2,2] => 111111111100 => 111111111001 => [1,1,1,1,1,1,1,1,1,3,1]
[4,4,4,4,4] => 111110000 => 111100001 => [1,1,1,1,5,1]
[4,4,4,3,3,3] => 1110111000 => 1101110001 => [1,1,2,1,1,4,1]
[4,4,4,4,4,4] => 1111110000 => 1111100001 => [1,1,1,1,1,5,1]
[5,5,5,5] => 111100000 => 111000001 => [1,1,1,6,1]
[6,6,6,6] => 1111000000 => 1110000001 => [1,1,1,7,1]
[6,6,6] => 111000000 => 110000001 => [1,1,7,1]
[10,10] => 110000000000 => 100000000001 => [1,11,1]
[8,6,4,2] => 100100100100 => 001001001001 => [3,3,3,3,1]
[5,5,5,5,5,5] => 11111100000 => 11111000001 => [1,1,1,1,1,6,1]
[7,7,7,7] => 11110000000 => 11100000001 => [1,1,1,8,1]
[8,7,6,5,4,3,2,1] => 1010101010101010 => 0101010101010101 => [2,2,2,2,2,2,2,2,1]
[9,8,7,6,5,4,3,2,1] => 101010101010101010 => 010101010101010101 => [2,2,2,2,2,2,2,2,2,1]
[5,5,5,5,5] => 1111100000 => 1111000001 => [1,1,1,1,6,1]
[9,9] => 11000000000 => 10000000001 => [1,10,1]
[6,5,5,5] => 1011100000 => 0111000001 => [2,1,1,6,1]
[5,4,4,4,4] => 1011110000 => 0111100001 => [2,1,1,1,5,1]
[4,4,4,4,4,1] => 1111100010 => 1111000101 => [1,1,1,1,4,2,1]
[5,5,5,5,1] => 1111000010 => 1110000101 => [1,1,1,5,2,1]
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
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.