Identifier
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
Mp00173: Integer compositions —rotate front to back⟶ Integer compositions
Images
[1] => 10 => [1,2] => [2,1]
[2] => 100 => [1,3] => [3,1]
[1,1] => 110 => [1,1,2] => [1,2,1]
[3] => 1000 => [1,4] => [4,1]
[2,1] => 1010 => [1,2,2] => [2,2,1]
[1,1,1] => 1110 => [1,1,1,2] => [1,1,2,1]
[4] => 10000 => [1,5] => [5,1]
[3,1] => 10010 => [1,3,2] => [3,2,1]
[2,2] => 1100 => [1,1,3] => [1,3,1]
[2,1,1] => 10110 => [1,2,1,2] => [2,1,2,1]
[1,1,1,1] => 11110 => [1,1,1,1,2] => [1,1,1,2,1]
[5] => 100000 => [1,6] => [6,1]
[4,1] => 100010 => [1,4,2] => [4,2,1]
[3,2] => 10100 => [1,2,3] => [2,3,1]
[3,1,1] => 100110 => [1,3,1,2] => [3,1,2,1]
[2,2,1] => 11010 => [1,1,2,2] => [1,2,2,1]
[2,1,1,1] => 101110 => [1,2,1,1,2] => [2,1,1,2,1]
[1,1,1,1,1] => 111110 => [1,1,1,1,1,2] => [1,1,1,1,2,1]
[6] => 1000000 => [1,7] => [7,1]
[5,1] => 1000010 => [1,5,2] => [5,2,1]
[4,2] => 100100 => [1,3,3] => [3,3,1]
[4,1,1] => 1000110 => [1,4,1,2] => [4,1,2,1]
[3,3] => 11000 => [1,1,4] => [1,4,1]
[3,2,1] => 101010 => [1,2,2,2] => [2,2,2,1]
[3,1,1,1] => 1001110 => [1,3,1,1,2] => [3,1,1,2,1]
[2,2,2] => 11100 => [1,1,1,3] => [1,1,3,1]
[2,2,1,1] => 110110 => [1,1,2,1,2] => [1,2,1,2,1]
[2,1,1,1,1] => 1011110 => [1,2,1,1,1,2] => [2,1,1,1,2,1]
[1,1,1,1,1,1] => 1111110 => [1,1,1,1,1,1,2] => [1,1,1,1,1,2,1]
[7] => 10000000 => [1,8] => [8,1]
[6,1] => 10000010 => [1,6,2] => [6,2,1]
[5,2] => 1000100 => [1,4,3] => [4,3,1]
[5,1,1] => 10000110 => [1,5,1,2] => [5,1,2,1]
[4,3] => 101000 => [1,2,4] => [2,4,1]
[4,2,1] => 1001010 => [1,3,2,2] => [3,2,2,1]
[4,1,1,1] => 10001110 => [1,4,1,1,2] => [4,1,1,2,1]
[3,3,1] => 110010 => [1,1,3,2] => [1,3,2,1]
[3,2,2] => 101100 => [1,2,1,3] => [2,1,3,1]
[3,2,1,1] => 1010110 => [1,2,2,1,2] => [2,2,1,2,1]
[3,1,1,1,1] => 10011110 => [1,3,1,1,1,2] => [3,1,1,1,2,1]
[2,2,2,1] => 111010 => [1,1,1,2,2] => [1,1,2,2,1]
[2,2,1,1,1] => 1101110 => [1,1,2,1,1,2] => [1,2,1,1,2,1]
[2,1,1,1,1,1] => 10111110 => [1,2,1,1,1,1,2] => [2,1,1,1,1,2,1]
[1,1,1,1,1,1,1] => 11111110 => [1,1,1,1,1,1,1,2] => [1,1,1,1,1,1,2,1]
[8] => 100000000 => [1,9] => [9,1]
[7,1] => 100000010 => [1,7,2] => [7,2,1]
[6,2] => 10000100 => [1,5,3] => [5,3,1]
[6,1,1] => 100000110 => [1,6,1,2] => [6,1,2,1]
[5,3] => 1001000 => [1,3,4] => [3,4,1]
[5,2,1] => 10001010 => [1,4,2,2] => [4,2,2,1]
[5,1,1,1] => 100001110 => [1,5,1,1,2] => [5,1,1,2,1]
[4,4] => 110000 => [1,1,5] => [1,5,1]
[4,3,1] => 1010010 => [1,2,3,2] => [2,3,2,1]
[4,2,2] => 1001100 => [1,3,1,3] => [3,1,3,1]
[4,2,1,1] => 10010110 => [1,3,2,1,2] => [3,2,1,2,1]
[4,1,1,1,1] => 100011110 => [1,4,1,1,1,2] => [4,1,1,1,2,1]
[3,3,2] => 110100 => [1,1,2,3] => [1,2,3,1]
[3,3,1,1] => 1100110 => [1,1,3,1,2] => [1,3,1,2,1]
[3,2,2,1] => 1011010 => [1,2,1,2,2] => [2,1,2,2,1]
[3,2,1,1,1] => 10101110 => [1,2,2,1,1,2] => [2,2,1,1,2,1]
[3,1,1,1,1,1] => 100111110 => [1,3,1,1,1,1,2] => [3,1,1,1,1,2,1]
[2,2,2,2] => 111100 => [1,1,1,1,3] => [1,1,1,3,1]
[2,2,2,1,1] => 1110110 => [1,1,1,2,1,2] => [1,1,2,1,2,1]
[2,2,1,1,1,1] => 11011110 => [1,1,2,1,1,1,2] => [1,2,1,1,1,2,1]
[2,1,1,1,1,1,1] => 101111110 => [1,2,1,1,1,1,1,2] => [2,1,1,1,1,1,2,1]
[1,1,1,1,1,1,1,1] => 111111110 => [1,1,1,1,1,1,1,1,2] => [1,1,1,1,1,1,1,2,1]
[9] => 1000000000 => [1,10] => [10,1]
[8,1] => 1000000010 => [1,8,2] => [8,2,1]
[7,2] => 100000100 => [1,6,3] => [6,3,1]
[7,1,1] => 1000000110 => [1,7,1,2] => [7,1,2,1]
[6,3] => 10001000 => [1,4,4] => [4,4,1]
[6,2,1] => 100001010 => [1,5,2,2] => [5,2,2,1]
[6,1,1,1] => 1000001110 => [1,6,1,1,2] => [6,1,1,2,1]
[5,4] => 1010000 => [1,2,5] => [2,5,1]
[5,3,1] => 10010010 => [1,3,3,2] => [3,3,2,1]
[5,2,2] => 10001100 => [1,4,1,3] => [4,1,3,1]
[5,2,1,1] => 100010110 => [1,4,2,1,2] => [4,2,1,2,1]
[5,1,1,1,1] => 1000011110 => [1,5,1,1,1,2] => [5,1,1,1,2,1]
[4,4,1] => 1100010 => [1,1,4,2] => [1,4,2,1]
[4,3,2] => 1010100 => [1,2,2,3] => [2,2,3,1]
[4,3,1,1] => 10100110 => [1,2,3,1,2] => [2,3,1,2,1]
[4,2,2,1] => 10011010 => [1,3,1,2,2] => [3,1,2,2,1]
[4,2,1,1,1] => 100101110 => [1,3,2,1,1,2] => [3,2,1,1,2,1]
[4,1,1,1,1,1] => 1000111110 => [1,4,1,1,1,1,2] => [4,1,1,1,1,2,1]
[3,3,3] => 111000 => [1,1,1,4] => [1,1,4,1]
[3,3,2,1] => 1101010 => [1,1,2,2,2] => [1,2,2,2,1]
[3,3,1,1,1] => 11001110 => [1,1,3,1,1,2] => [1,3,1,1,2,1]
[3,2,2,2] => 1011100 => [1,2,1,1,3] => [2,1,1,3,1]
[3,2,2,1,1] => 10110110 => [1,2,1,2,1,2] => [2,1,2,1,2,1]
[3,2,1,1,1,1] => 101011110 => [1,2,2,1,1,1,2] => [2,2,1,1,1,2,1]
[3,1,1,1,1,1,1] => 1001111110 => [1,3,1,1,1,1,1,2] => [3,1,1,1,1,1,2,1]
[2,2,2,2,1] => 1111010 => [1,1,1,1,2,2] => [1,1,1,2,2,1]
[2,2,2,1,1,1] => 11101110 => [1,1,1,2,1,1,2] => [1,1,2,1,1,2,1]
[2,2,1,1,1,1,1] => 110111110 => [1,1,2,1,1,1,1,2] => [1,2,1,1,1,1,2,1]
[2,1,1,1,1,1,1,1] => 1011111110 => [1,2,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,2,1]
[1,1,1,1,1,1,1,1,1] => 1111111110 => [1,1,1,1,1,1,1,1,1,2] => [1,1,1,1,1,1,1,1,2,1]
[10] => 10000000000 => [1,11] => [11,1]
[9,1] => 10000000010 => [1,9,2] => [9,2,1]
[8,2] => 1000000100 => [1,7,3] => [7,3,1]
[8,1,1] => 10000000110 => [1,8,1,2] => [8,1,2,1]
[7,3] => 100001000 => [1,5,4] => [5,4,1]
>>> Load all 366 entries. <<<
[7,2,1] => 1000001010 => [1,6,2,2] => [6,2,2,1]
[7,1,1,1] => 10000001110 => [1,7,1,1,2] => [7,1,1,2,1]
[6,4] => 10010000 => [1,3,5] => [3,5,1]
[6,3,1] => 100010010 => [1,4,3,2] => [4,3,2,1]
[6,2,2] => 100001100 => [1,5,1,3] => [5,1,3,1]
[6,2,1,1] => 1000010110 => [1,5,2,1,2] => [5,2,1,2,1]
[6,1,1,1,1] => 10000011110 => [1,6,1,1,1,2] => [6,1,1,1,2,1]
[5,5] => 1100000 => [1,1,6] => [1,6,1]
[5,4,1] => 10100010 => [1,2,4,2] => [2,4,2,1]
[5,3,2] => 10010100 => [1,3,2,3] => [3,2,3,1]
[5,3,1,1] => 100100110 => [1,3,3,1,2] => [3,3,1,2,1]
[5,2,2,1] => 100011010 => [1,4,1,2,2] => [4,1,2,2,1]
[5,2,1,1,1] => 1000101110 => [1,4,2,1,1,2] => [4,2,1,1,2,1]
[5,1,1,1,1,1] => 10000111110 => [1,5,1,1,1,1,2] => [5,1,1,1,1,2,1]
[4,4,2] => 1100100 => [1,1,3,3] => [1,3,3,1]
[4,4,1,1] => 11000110 => [1,1,4,1,2] => [1,4,1,2,1]
[4,3,3] => 1011000 => [1,2,1,4] => [2,1,4,1]
[4,3,2,1] => 10101010 => [1,2,2,2,2] => [2,2,2,2,1]
[4,3,1,1,1] => 101001110 => [1,2,3,1,1,2] => [2,3,1,1,2,1]
[4,2,2,2] => 10011100 => [1,3,1,1,3] => [3,1,1,3,1]
[4,2,2,1,1] => 100110110 => [1,3,1,2,1,2] => [3,1,2,1,2,1]
[4,2,1,1,1,1] => 1001011110 => [1,3,2,1,1,1,2] => [3,2,1,1,1,2,1]
[4,1,1,1,1,1,1] => 10001111110 => [1,4,1,1,1,1,1,2] => [4,1,1,1,1,1,2,1]
[3,3,3,1] => 1110010 => [1,1,1,3,2] => [1,1,3,2,1]
[3,3,2,2] => 1101100 => [1,1,2,1,3] => [1,2,1,3,1]
[3,3,2,1,1] => 11010110 => [1,1,2,2,1,2] => [1,2,2,1,2,1]
[3,3,1,1,1,1] => 110011110 => [1,1,3,1,1,1,2] => [1,3,1,1,1,2,1]
[3,2,2,2,1] => 10111010 => [1,2,1,1,2,2] => [2,1,1,2,2,1]
[3,2,2,1,1,1] => 101101110 => [1,2,1,2,1,1,2] => [2,1,2,1,1,2,1]
[3,2,1,1,1,1,1] => 1010111110 => [1,2,2,1,1,1,1,2] => [2,2,1,1,1,1,2,1]
[3,1,1,1,1,1,1,1] => 10011111110 => [1,3,1,1,1,1,1,1,2] => [3,1,1,1,1,1,1,2,1]
[2,2,2,2,2] => 1111100 => [1,1,1,1,1,3] => [1,1,1,1,3,1]
[2,2,2,2,1,1] => 11110110 => [1,1,1,1,2,1,2] => [1,1,1,2,1,2,1]
[2,2,2,1,1,1,1] => 111011110 => [1,1,1,2,1,1,1,2] => [1,1,2,1,1,1,2,1]
[2,2,1,1,1,1,1,1] => 1101111110 => [1,1,2,1,1,1,1,1,2] => [1,2,1,1,1,1,1,2,1]
[2,1,1,1,1,1,1,1,1] => 10111111110 => [1,2,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,2,1]
[1,1,1,1,1,1,1,1,1,1] => 11111111110 => [1,1,1,1,1,1,1,1,1,1,2] => [1,1,1,1,1,1,1,1,1,2,1]
[9,2] => 10000000100 => [1,8,3] => [8,3,1]
[7,4] => 100010000 => [1,4,5] => [4,5,1]
[6,5] => 10100000 => [1,2,6] => [2,6,1]
[6,4,1] => 100100010 => [1,3,4,2] => [3,4,2,1]
[6,3,2] => 100010100 => [1,4,2,3] => [4,2,3,1]
[5,5,1] => 11000010 => [1,1,5,2] => [1,5,2,1]
[5,4,2] => 10100100 => [1,2,3,3] => [2,3,3,1]
[5,4,1,1] => 101000110 => [1,2,4,1,2] => [2,4,1,2,1]
[5,3,3] => 10011000 => [1,3,1,4] => [3,1,4,1]
[5,3,2,1] => 100101010 => [1,3,2,2,2] => [3,2,2,2,1]
[5,2,2,2] => 100011100 => [1,4,1,1,3] => [4,1,1,3,1]
[4,4,3] => 1101000 => [1,1,2,4] => [1,2,4,1]
[4,4,2,1] => 11001010 => [1,1,3,2,2] => [1,3,2,2,1]
[4,4,1,1,1] => 110001110 => [1,1,4,1,1,2] => [1,4,1,1,2,1]
[4,3,3,1] => 10110010 => [1,2,1,3,2] => [2,1,3,2,1]
[4,3,2,2] => 10101100 => [1,2,2,1,3] => [2,2,1,3,1]
[4,3,2,1,1] => 101010110 => [1,2,2,2,1,2] => [2,2,2,1,2,1]
[4,2,2,2,1] => 100111010 => [1,3,1,1,2,2] => [3,1,1,2,2,1]
[3,3,3,2] => 1110100 => [1,1,1,2,3] => [1,1,2,3,1]
[3,3,3,1,1] => 11100110 => [1,1,1,3,1,2] => [1,1,3,1,2,1]
[3,3,2,2,1] => 11011010 => [1,1,2,1,2,2] => [1,2,1,2,2,1]
[3,3,2,1,1,1] => 110101110 => [1,1,2,2,1,1,2] => [1,2,2,1,1,2,1]
[3,2,2,2,2] => 10111100 => [1,2,1,1,1,3] => [2,1,1,1,3,1]
[3,2,2,2,1,1] => 101110110 => [1,2,1,1,2,1,2] => [2,1,1,2,1,2,1]
[2,2,2,2,2,1] => 11111010 => [1,1,1,1,1,2,2] => [1,1,1,1,2,2,1]
[2,2,2,2,1,1,1] => 111101110 => [1,1,1,1,2,1,1,2] => [1,1,1,2,1,1,2,1]
[2,2,1,1,1,1,1,1,1] => 11011111110 => [1,1,2,1,1,1,1,1,1,2] => [1,2,1,1,1,1,1,1,2,1]
[8,4] => 1000010000 => [1,5,5] => [5,5,1]
[7,5] => 100100000 => [1,3,6] => [3,6,1]
[6,6] => 11000000 => [1,1,7] => [1,7,1]
[6,5,1] => 101000010 => [1,2,5,2] => [2,5,2,1]
[6,4,2] => 100100100 => [1,3,3,3] => [3,3,3,1]
[6,3,3] => 100011000 => [1,4,1,4] => [4,1,4,1]
[5,5,2] => 11000100 => [1,1,4,3] => [1,4,3,1]
[5,5,1,1] => 110000110 => [1,1,5,1,2] => [1,5,1,2,1]
[5,4,3] => 10101000 => [1,2,2,4] => [2,2,4,1]
[5,4,2,1] => 101001010 => [1,2,3,2,2] => [2,3,2,2,1]
[5,3,3,1] => 100110010 => [1,3,1,3,2] => [3,1,3,2,1]
[5,3,2,2] => 100101100 => [1,3,2,1,3] => [3,2,1,3,1]
[4,4,4] => 1110000 => [1,1,1,5] => [1,1,5,1]
[4,4,3,1] => 11010010 => [1,1,2,3,2] => [1,2,3,2,1]
[4,4,2,2] => 11001100 => [1,1,3,1,3] => [1,3,1,3,1]
[4,4,2,1,1] => 110010110 => [1,1,3,2,1,2] => [1,3,2,1,2,1]
[4,3,3,2] => 10110100 => [1,2,1,2,3] => [2,1,2,3,1]
[4,3,3,1,1] => 101100110 => [1,2,1,3,1,2] => [2,1,3,1,2,1]
[4,3,2,2,1] => 101011010 => [1,2,2,1,2,2] => [2,2,1,2,2,1]
[4,2,2,2,2] => 100111100 => [1,3,1,1,1,3] => [3,1,1,1,3,1]
[3,3,3,3] => 1111000 => [1,1,1,1,4] => [1,1,1,4,1]
[3,3,3,2,1] => 11101010 => [1,1,1,2,2,2] => [1,1,2,2,2,1]
[3,3,3,1,1,1] => 111001110 => [1,1,1,3,1,1,2] => [1,1,3,1,1,2,1]
[3,3,2,2,2] => 11011100 => [1,1,2,1,1,3] => [1,2,1,1,3,1]
[3,3,2,2,1,1] => 110110110 => [1,1,2,1,2,1,2] => [1,2,1,2,1,2,1]
[3,2,2,2,2,1] => 101111010 => [1,2,1,1,1,2,2] => [2,1,1,1,2,2,1]
[2,2,2,2,2,2] => 11111100 => [1,1,1,1,1,1,3] => [1,1,1,1,1,3,1]
[2,2,2,2,2,1,1] => 111110110 => [1,1,1,1,1,2,1,2] => [1,1,1,1,2,1,2,1]
[9,4] => 10000010000 => [1,6,5] => [6,5,1]
[8,5] => 1000100000 => [1,4,6] => [4,6,1]
[8,4,1] => 10000100010 => [1,5,4,2] => [5,4,2,1]
[7,6] => 101000000 => [1,2,7] => [2,7,1]
[6,6,1] => 110000010 => [1,1,6,2] => [1,6,2,1]
[6,5,2] => 101000100 => [1,2,4,3] => [2,4,3,1]
[6,4,3] => 100101000 => [1,3,2,4] => [3,2,4,1]
[5,5,3] => 11001000 => [1,1,3,4] => [1,3,4,1]
[5,5,2,1] => 110001010 => [1,1,4,2,2] => [1,4,2,2,1]
[5,4,4] => 10110000 => [1,2,1,5] => [2,1,5,1]
[5,4,3,1] => 101010010 => [1,2,2,3,2] => [2,2,3,2,1]
[5,4,2,2] => 101001100 => [1,2,3,1,3] => [2,3,1,3,1]
[5,3,3,2] => 100110100 => [1,3,1,2,3] => [3,1,2,3,1]
[4,4,4,1] => 11100010 => [1,1,1,4,2] => [1,1,4,2,1]
[4,4,3,2] => 11010100 => [1,1,2,2,3] => [1,2,2,3,1]
[4,4,3,1,1] => 110100110 => [1,1,2,3,1,2] => [1,2,3,1,2,1]
[4,4,2,2,1] => 110011010 => [1,1,3,1,2,2] => [1,3,1,2,2,1]
[4,3,3,3] => 10111000 => [1,2,1,1,4] => [2,1,1,4,1]
[4,3,3,2,1] => 101101010 => [1,2,1,2,2,2] => [2,1,2,2,2,1]
[4,3,2,2,2] => 101011100 => [1,2,2,1,1,3] => [2,2,1,1,3,1]
[3,3,3,3,1] => 11110010 => [1,1,1,1,3,2] => [1,1,1,3,2,1]
[3,3,3,2,2] => 11101100 => [1,1,1,2,1,3] => [1,1,2,1,3,1]
[3,3,3,2,1,1] => 111010110 => [1,1,1,2,2,1,2] => [1,1,2,2,1,2,1]
[3,3,2,2,2,1] => 110111010 => [1,1,2,1,1,2,2] => [1,2,1,1,2,2,1]
[3,2,2,2,2,2] => 101111100 => [1,2,1,1,1,1,3] => [2,1,1,1,1,3,1]
[3,2,2,2,1,1,1,1] => 10111011110 => [1,2,1,1,2,1,1,1,2] => [2,1,1,2,1,1,1,2,1]
[2,2,2,2,2,2,1] => 111111010 => [1,1,1,1,1,1,2,2] => [1,1,1,1,1,2,2,1]
[2,2,2,2,1,1,1,1,1] => 11110111110 => [1,1,1,1,2,1,1,1,1,2] => [1,1,1,2,1,1,1,1,2,1]
[8,6] => 1001000000 => [1,3,7] => [3,7,1]
[8,5,1] => 10001000010 => [1,4,5,2] => [4,5,2,1]
[8,4,2] => 10000100100 => [1,5,3,3] => [5,3,3,1]
[7,7] => 110000000 => [1,1,8] => [1,8,1]
[7,4,2,1] => 10001001010 => [1,4,3,2,2] => [4,3,2,2,1]
[6,6,2] => 110000100 => [1,1,5,3] => [1,5,3,1]
[6,5,3] => 101001000 => [1,2,3,4] => [2,3,4,1]
[6,4,4] => 100110000 => [1,3,1,5] => [3,1,5,1]
[5,5,4] => 11010000 => [1,1,2,5] => [1,2,5,1]
[5,5,3,1] => 110010010 => [1,1,3,3,2] => [1,3,3,2,1]
[5,5,2,2] => 110001100 => [1,1,4,1,3] => [1,4,1,3,1]
[5,4,4,1] => 101100010 => [1,2,1,4,2] => [2,1,4,2,1]
[5,4,3,2] => 101010100 => [1,2,2,2,3] => [2,2,2,3,1]
[5,3,3,3] => 100111000 => [1,3,1,1,4] => [3,1,1,4,1]
[4,4,4,2] => 11100100 => [1,1,1,3,3] => [1,1,3,3,1]
[4,4,4,1,1] => 111000110 => [1,1,1,4,1,2] => [1,1,4,1,2,1]
[4,4,3,3] => 11011000 => [1,1,2,1,4] => [1,2,1,4,1]
[4,4,3,2,1] => 110101010 => [1,1,2,2,2,2] => [1,2,2,2,2,1]
[4,4,2,2,2] => 110011100 => [1,1,3,1,1,3] => [1,3,1,1,3,1]
[4,3,3,3,1] => 101110010 => [1,2,1,1,3,2] => [2,1,1,3,2,1]
[4,3,3,2,2] => 101101100 => [1,2,1,2,1,3] => [2,1,2,1,3,1]
[4,3,2,2,1,1,1] => 10101101110 => [1,2,2,1,2,1,1,2] => [2,2,1,2,1,1,2,1]
[3,3,3,3,2] => 11110100 => [1,1,1,1,2,3] => [1,1,1,2,3,1]
[3,3,3,3,1,1] => 111100110 => [1,1,1,1,3,1,2] => [1,1,1,3,1,2,1]
[3,3,3,2,2,1] => 111011010 => [1,1,1,2,1,2,2] => [1,1,2,1,2,2,1]
[3,3,2,2,2,2] => 110111100 => [1,1,2,1,1,1,3] => [1,2,1,1,1,3,1]
[3,3,2,2,1,1,1,1] => 11011011110 => [1,1,2,1,2,1,1,1,2] => [1,2,1,2,1,1,1,2,1]
[3,2,2,2,2,1,1,1] => 10111101110 => [1,2,1,1,1,2,1,1,2] => [2,1,1,1,2,1,1,2,1]
[2,2,2,2,2,2,2] => 111111100 => [1,1,1,1,1,1,1,3] => [1,1,1,1,1,1,3,1]
[8,7] => 1010000000 => [1,2,8] => [2,8,1]
[8,5,2] => 10001000100 => [1,4,4,3] => [4,4,3,1]
[8,4,3] => 10000101000 => [1,5,2,4] => [5,2,4,1]
[7,5,2,1] => 10010001010 => [1,3,4,2,2] => [3,4,2,2,1]
[7,4,3,1] => 10001010010 => [1,4,2,3,2] => [4,2,3,2,1]
[6,6,3] => 110001000 => [1,1,4,4] => [1,4,4,1]
[6,5,4] => 101010000 => [1,2,2,5] => [2,2,5,1]
[5,5,5] => 11100000 => [1,1,1,6] => [1,1,6,1]
[5,5,4,1] => 110100010 => [1,1,2,4,2] => [1,2,4,2,1]
[5,5,3,2] => 110010100 => [1,1,3,2,3] => [1,3,2,3,1]
[5,4,4,2] => 101100100 => [1,2,1,3,3] => [2,1,3,3,1]
[5,4,3,3] => 101011000 => [1,2,2,1,4] => [2,2,1,4,1]
[5,4,3,2,1] => 1010101010 => [1,2,2,2,2,2] => [2,2,2,2,2,1]
[4,4,4,3] => 11101000 => [1,1,1,2,4] => [1,1,2,4,1]
[4,4,4,2,1] => 111001010 => [1,1,1,3,2,2] => [1,1,3,2,2,1]
[4,4,3,3,1] => 110110010 => [1,1,2,1,3,2] => [1,2,1,3,2,1]
[4,4,3,2,2] => 110101100 => [1,1,2,2,1,3] => [1,2,2,1,3,1]
[4,3,3,3,2] => 101110100 => [1,2,1,1,2,3] => [2,1,1,2,3,1]
[4,3,3,2,1,1,1] => 10110101110 => [1,2,1,2,2,1,1,2] => [2,1,2,2,1,1,2,1]
[4,3,2,2,2,1,1] => 10101110110 => [1,2,2,1,1,2,1,2] => [2,2,1,1,2,1,2,1]
[3,3,3,3,3] => 11111000 => [1,1,1,1,1,4] => [1,1,1,1,4,1]
[3,3,3,3,2,1] => 111101010 => [1,1,1,1,2,2,2] => [1,1,1,2,2,2,1]
[3,3,3,2,2,2] => 111011100 => [1,1,1,2,1,1,3] => [1,1,2,1,1,3,1]
[3,3,3,2,1,1,1,1] => 11101011110 => [1,1,1,2,2,1,1,1,2] => [1,1,2,2,1,1,1,2,1]
[3,3,2,2,2,1,1,1] => 11011101110 => [1,1,2,1,1,2,1,1,2] => [1,2,1,1,2,1,1,2,1]
[2,2,2,2,2,2,1,1,1] => 11111101110 => [1,1,1,1,1,1,2,1,1,2] => [1,1,1,1,1,2,1,1,2,1]
[8,8] => 1100000000 => [1,1,9] => [1,9,1]
[8,6,2] => 10010000100 => [1,3,5,3] => [3,5,3,1]
[8,5,3] => 10001001000 => [1,4,3,4] => [4,3,4,1]
[7,5,3,1] => 10010010010 => [1,3,3,3,2] => [3,3,3,2,1]
[7,4,3,2] => 10001010100 => [1,4,2,2,3] => [4,2,2,3,1]
[6,6,4] => 110010000 => [1,1,3,5] => [1,3,5,1]
[6,5,5] => 101100000 => [1,2,1,6] => [2,1,6,1]
[6,4,3,2,1] => 10010101010 => [1,3,2,2,2,2] => [3,2,2,2,2,1]
[5,5,5,1] => 111000010 => [1,1,1,5,2] => [1,1,5,2,1]
[5,5,4,2] => 110100100 => [1,1,2,3,3] => [1,2,3,3,1]
[5,5,3,3] => 110011000 => [1,1,3,1,4] => [1,3,1,4,1]
[5,5,3,2,1] => 1100101010 => [1,1,3,2,2,2] => [1,3,2,2,2,1]
[5,4,4,3] => 101101000 => [1,2,1,2,4] => [2,1,2,4,1]
[5,4,4,2,1] => 1011001010 => [1,2,1,3,2,2] => [2,1,3,2,2,1]
[5,4,3,3,1] => 1010110010 => [1,2,2,1,3,2] => [2,2,1,3,2,1]
[5,4,3,2,2] => 1010101100 => [1,2,2,2,1,3] => [2,2,2,1,3,1]
[5,4,3,2,1,1] => 10101010110 => [1,2,2,2,2,1,2] => [2,2,2,2,1,2,1]
[4,4,4,4] => 11110000 => [1,1,1,1,5] => [1,1,1,5,1]
[4,4,4,3,1] => 111010010 => [1,1,1,2,3,2] => [1,1,2,3,2,1]
[4,4,4,2,2] => 111001100 => [1,1,1,3,1,3] => [1,1,3,1,3,1]
[4,4,3,3,2] => 110110100 => [1,1,2,1,2,3] => [1,2,1,2,3,1]
[4,4,3,2,1,1,1] => 11010101110 => [1,1,2,2,2,1,1,2] => [1,2,2,2,1,1,2,1]
[4,3,3,3,3] => 101111000 => [1,2,1,1,1,4] => [2,1,1,1,4,1]
[4,3,3,2,2,1,1] => 10110110110 => [1,2,1,2,1,2,1,2] => [2,1,2,1,2,1,2,1]
[3,3,3,3,3,1] => 111110010 => [1,1,1,1,1,3,2] => [1,1,1,1,3,2,1]
[3,3,3,3,2,2] => 111101100 => [1,1,1,1,2,1,3] => [1,1,1,2,1,3,1]
[3,3,3,2,2,1,1,1] => 11101101110 => [1,1,1,2,1,2,1,1,2] => [1,1,2,1,2,1,1,2,1]
[3,3,2,2,2,2,1,1] => 11011110110 => [1,1,2,1,1,1,2,1,2] => [1,2,1,1,1,2,1,2,1]
[2,2,2,2,2,2,2,2] => 1111111100 => [1,1,1,1,1,1,1,1,3] => [1,1,1,1,1,1,1,3,1]
[9,8] => 10100000000 => [1,2,9] => [2,9,1]
[8,6,3] => 10010001000 => [1,3,4,4] => [3,4,4,1]
[7,6,3,1] => 10100010010 => [1,2,4,3,2] => [2,4,3,2,1]
[7,5,4,1] => 10010100010 => [1,3,2,4,2] => [3,2,4,2,1]
[7,5,3,2] => 10010010100 => [1,3,3,2,3] => [3,3,2,3,1]
[6,6,5] => 110100000 => [1,1,2,6] => [1,2,6,1]
[6,5,3,2,1] => 10100101010 => [1,2,3,2,2,2] => [2,3,2,2,2,1]
[5,5,5,2] => 111000100 => [1,1,1,4,3] => [1,1,4,3,1]
[5,5,4,3] => 110101000 => [1,1,2,2,4] => [1,2,2,4,1]
[5,5,4,2,1] => 1101001010 => [1,1,2,3,2,2] => [1,2,3,2,2,1]
[5,5,3,3,1] => 1100110010 => [1,1,3,1,3,2] => [1,3,1,3,2,1]
[5,5,3,2,2] => 1100101100 => [1,1,3,2,1,3] => [1,3,2,1,3,1]
[5,4,4,4] => 101110000 => [1,2,1,1,5] => [2,1,1,5,1]
[5,4,4,3,1] => 1011010010 => [1,2,1,2,3,2] => [2,1,2,3,2,1]
[5,4,4,2,2] => 1011001100 => [1,2,1,3,1,3] => [2,1,3,1,3,1]
[5,4,3,3,2] => 1010110100 => [1,2,2,1,2,3] => [2,2,1,2,3,1]
[5,4,3,2,2,1] => 10101011010 => [1,2,2,2,1,2,2] => [2,2,2,1,2,2,1]
[4,4,4,4,1] => 111100010 => [1,1,1,1,4,2] => [1,1,1,4,2,1]
[4,4,4,3,2] => 111010100 => [1,1,1,2,2,3] => [1,1,2,2,3,1]
[4,4,3,3,3] => 110111000 => [1,1,2,1,1,4] => [1,2,1,1,4,1]
[4,4,3,2,2,1,1] => 11010110110 => [1,1,2,2,1,2,1,2] => [1,2,2,1,2,1,2,1]
[4,3,3,3,2,1,1] => 10111010110 => [1,2,1,1,2,2,1,2] => [2,1,1,2,2,1,2,1]
[4,3,3,2,2,2,1] => 10110111010 => [1,2,1,2,1,1,2,2] => [2,1,2,1,1,2,2,1]
[3,3,3,3,3,2] => 111110100 => [1,1,1,1,1,2,3] => [1,1,1,1,2,3,1]
[3,3,3,2,2,2,1,1] => 11101110110 => [1,1,1,2,1,1,2,1,2] => [1,1,2,1,1,2,1,2,1]
[2,2,2,2,2,2,2,2,1] => 11111111010 => [1,1,1,1,1,1,1,1,2,2] => [1,1,1,1,1,1,1,2,2,1]
[] => => [1] => [1]
[6,5,4,3,2,1] => 101010101010 => [1,2,2,2,2,2,2] => [2,2,2,2,2,2,1]
[5,5,4,3,2,1] => 11010101010 => [1,1,2,2,2,2,2] => [1,2,2,2,2,2,1]
[5,4,4,3,2,1] => 10110101010 => [1,2,1,2,2,2,2] => [2,1,2,2,2,2,1]
[5,4,3,3,2,1] => 10101101010 => [1,2,2,1,2,2,2] => [2,2,1,2,2,2,1]
[6,5,4,3,2] => 10101010100 => [1,2,2,2,2,3] => [2,2,2,2,3,1]
[5,5,4,3,2] => 1101010100 => [1,1,2,2,2,3] => [1,2,2,2,3,1]
[5,4,4,3,2] => 1011010100 => [1,2,1,2,2,3] => [2,1,2,2,3,1]
[5,5,3,3,2] => 1100110100 => [1,1,3,1,2,3] => [1,3,1,2,3,1]
[5,5,4,2,2] => 1101001100 => [1,1,2,3,1,3] => [1,2,3,1,3,1]
[6,5,4,3,1] => 10101010010 => [1,2,2,2,3,2] => [2,2,2,3,2,1]
[5,5,4,3,1] => 1101010010 => [1,1,2,2,3,2] => [1,2,2,3,2,1]
[6,5,4,2,1] => 10101001010 => [1,2,2,3,2,2] => [2,2,3,2,2,1]
[6,6,5,4,3,2] => 110101010100 => [1,1,2,2,2,2,3] => [1,2,2,2,2,3,1]
[6,5,5,4,3,2] => 101101010100 => [1,2,1,2,2,2,3] => [2,1,2,2,2,3,1]
[5,5,5,4,3,2] => 11101010100 => [1,1,1,2,2,2,3] => [1,1,2,2,2,3,1]
[6,5,4,4,3,2] => 101011010100 => [1,2,2,1,2,2,3] => [2,2,1,2,2,3,1]
[6,5,4,3,3,2] => 101010110100 => [1,2,2,2,1,2,3] => [2,2,2,1,2,3,1]
[6,5,4,3,2,2] => 101010101100 => [1,2,2,2,2,1,3] => [2,2,2,2,1,3,1]
[6,6,5,4,3,1] => 110101010010 => [1,1,2,2,2,3,2] => [1,2,2,2,3,2,1]
[6,5,5,4,3,1] => 101101010010 => [1,2,1,2,2,3,2] => [2,1,2,2,3,2,1]
[6,6,5,3,2,1] => 110100101010 => [1,1,2,3,2,2,2] => [1,2,3,2,2,2,1]
[6,6,4,3,2,1] => 110010101010 => [1,1,3,2,2,2,2] => [1,3,2,2,2,2,1]
[6,6,5,4,3] => 11010101000 => [1,1,2,2,2,4] => [1,2,2,2,4,1]
[5,4,4,4,3] => 1011101000 => [1,2,1,1,2,4] => [2,1,1,2,4,1]
[5,4,3,3,3] => 1010111000 => [1,2,2,1,1,4] => [2,2,1,1,4,1]
[4,4,4,4,2] => 111100100 => [1,1,1,1,3,3] => [1,1,1,3,3,1]
[7,6,5,2] => 10101000100 => [1,2,2,4,3] => [2,2,4,3,1]
[3,3,3,3,3,3] => 111111000 => [1,1,1,1,1,1,4] => [1,1,1,1,1,4,1]
[4,4,4,4,4] => 111110000 => [1,1,1,1,1,5] => [1,1,1,1,5,1]
[5,5,5,5] => 111100000 => [1,1,1,1,6] => [1,1,1,6,1]
[6,6,6] => 111000000 => [1,1,1,7] => [1,1,7,1]
[5,5,5,5,5] => 1111100000 => [1,1,1,1,1,6] => [1,1,1,1,6,1]
[5,4,4,4,4] => 1011110000 => [1,2,1,1,1,5] => [2,1,1,1,5,1]
[5,5,5,5,1] => 1111000010 => [1,1,1,1,5,2] => [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
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.
Map
rotate front to back
Description
The front to back rotation of the entries of an integer composition.