Identifier
Identifier
Mp00094: Integer compositions to binary wordBinary words
Images
[1] => 1
[1,1] => 11
[2] => 10
[1,1,1] => 111
[1,2] => 110
[2,1] => 101
[3] => 100
[1,1,1,1] => 1111
[1,1,2] => 1110
[1,2,1] => 1101
[1,3] => 1100
[2,1,1] => 1011
[2,2] => 1010
[3,1] => 1001
[4] => 1000
[1,1,1,1,1] => 11111
[1,1,1,2] => 11110
[1,1,2,1] => 11101
[1,1,3] => 11100
[1,2,1,1] => 11011
[1,2,2] => 11010
[1,3,1] => 11001
[1,4] => 11000
[2,1,1,1] => 10111
[2,1,2] => 10110
[2,2,1] => 10101
[2,3] => 10100
[3,1,1] => 10011
[3,2] => 10010
[4,1] => 10001
[5] => 10000
[1,1,1,1,1,1] => 111111
[1,1,1,1,2] => 111110
[1,1,1,2,1] => 111101
[1,1,1,3] => 111100
[1,1,2,1,1] => 111011
[1,1,2,2] => 111010
[1,1,3,1] => 111001
[1,1,4] => 111000
[1,2,1,1,1] => 110111
[1,2,1,2] => 110110
[1,2,2,1] => 110101
[1,2,3] => 110100
[1,3,1,1] => 110011
[1,3,2] => 110010
[1,4,1] => 110001
[1,5] => 110000
[2,1,1,1,1] => 101111
[2,1,1,2] => 101110
[2,1,2,1] => 101101
[2,1,3] => 101100
[2,2,1,1] => 101011
[2,2,2] => 101010
[2,3,1] => 101001
[2,4] => 101000
[3,1,1,1] => 100111
[3,1,2] => 100110
[3,2,1] => 100101
[3,3] => 100100
[4,1,1] => 100011
[4,2] => 100010
[5,1] => 100001
[6] => 100000
[1,1,1,1,1,1,1] => 1111111
[1,1,1,1,1,2] => 1111110
[1,1,1,1,2,1] => 1111101
[1,1,1,1,3] => 1111100
[1,1,1,2,1,1] => 1111011
[1,1,1,2,2] => 1111010
[1,1,1,3,1] => 1111001
[1,1,1,4] => 1111000
[1,1,2,1,1,1] => 1110111
[1,1,2,1,2] => 1110110
[1,1,2,2,1] => 1110101
[1,1,2,3] => 1110100
[1,1,3,1,1] => 1110011
[1,1,3,2] => 1110010
[1,1,4,1] => 1110001
[1,1,5] => 1110000
[1,2,1,1,1,1] => 1101111
[1,2,1,1,2] => 1101110
[1,2,1,2,1] => 1101101
[1,2,1,3] => 1101100
[1,2,2,1,1] => 1101011
[1,2,2,2] => 1101010
[1,2,3,1] => 1101001
[1,2,4] => 1101000
[1,3,1,1,1] => 1100111
[1,3,1,2] => 1100110
[1,3,2,1] => 1100101
[1,3,3] => 1100100
[1,4,1,1] => 1100011
[1,4,2] => 1100010
[1,5,1] => 1100001
[1,6] => 1100000
[2,1,1,1,1,1] => 1011111
[2,1,1,1,2] => 1011110
[2,1,1,2,1] => 1011101
[2,1,1,3] => 1011100
[2,1,2,1,1] => 1011011
[2,1,2,2] => 1011010
[2,1,3,1] => 1011001
[2,1,4] => 1011000
[2,2,1,1,1] => 1010111
[2,2,1,2] => 1010110
[2,2,2,1] => 1010101
[2,2,3] => 1010100
[2,3,1,1] => 1010011
[2,3,2] => 1010010
[2,4,1] => 1010001
[2,5] => 1010000
[3,1,1,1,1] => 1001111
[3,1,1,2] => 1001110
[3,1,2,1] => 1001101
[3,1,3] => 1001100
[3,2,1,1] => 1001011
[3,2,2] => 1001010
[3,3,1] => 1001001
[3,4] => 1001000
[4,1,1,1] => 1000111
[4,1,2] => 1000110
[4,2,1] => 1000101
[4,3] => 1000100
[5,1,1] => 1000011
[5,2] => 1000010
[6,1] => 1000001
[7] => 1000000
[1,1,1,1,1,1,1,1] => 11111111
[1,1,1,1,1,1,2] => 11111110
[1,1,1,1,1,2,1] => 11111101
[1,1,1,1,1,3] => 11111100
[1,1,1,1,2,1,1] => 11111011
[1,1,1,1,2,2] => 11111010
[1,1,1,1,3,1] => 11111001
[1,1,1,1,4] => 11111000
[1,1,1,2,1,1,1] => 11110111
[1,1,1,2,1,2] => 11110110
[1,1,1,2,2,1] => 11110101
[1,1,1,2,3] => 11110100
[1,1,1,3,1,1] => 11110011
[1,1,1,3,2] => 11110010
[1,1,1,4,1] => 11110001
[1,1,1,5] => 11110000
[1,1,2,1,1,1,1] => 11101111
[1,1,2,1,1,2] => 11101110
[1,1,2,1,2,1] => 11101101
[1,1,2,1,3] => 11101100
[1,1,2,2,1,1] => 11101011
[1,1,2,2,2] => 11101010
[1,1,2,3,1] => 11101001
[1,1,2,4] => 11101000
[1,1,3,1,1,1] => 11100111
[1,1,3,1,2] => 11100110
[1,1,3,2,1] => 11100101
[1,1,3,3] => 11100100
[1,1,4,1,1] => 11100011
[1,1,4,2] => 11100010
[1,1,5,1] => 11100001
[1,1,6] => 11100000
[1,2,1,1,1,1,1] => 11011111
[1,2,1,1,1,2] => 11011110
[1,2,1,1,2,1] => 11011101
[1,2,1,1,3] => 11011100
[1,2,1,2,1,1] => 11011011
[1,2,1,2,2] => 11011010
[1,2,1,3,1] => 11011001
[1,2,1,4] => 11011000
[1,2,2,1,1,1] => 11010111
[1,2,2,1,2] => 11010110
[1,2,2,2,1] => 11010101
[1,2,2,3] => 11010100
[1,2,3,1,1] => 11010011
[1,2,3,2] => 11010010
[1,2,4,1] => 11010001
[1,2,5] => 11010000
[1,3,1,1,1,1] => 11001111
[1,3,1,1,2] => 11001110
[1,3,1,2,1] => 11001101
[1,3,1,3] => 11001100
[1,3,2,1,1] => 11001011
[1,3,2,2] => 11001010
[1,3,3,1] => 11001001
[1,3,4] => 11001000
[1,4,1,1,1] => 11000111
[1,4,1,2] => 11000110
[1,4,2,1] => 11000101
[1,4,3] => 11000100
[1,5,1,1] => 11000011
[1,5,2] => 11000010
[1,6,1] => 11000001
[1,7] => 11000000
[2,1,1,1,1,1,1] => 10111111
[2,1,1,1,1,2] => 10111110
[2,1,1,1,2,1] => 10111101
[2,1,1,1,3] => 10111100
[2,1,1,2,1,1] => 10111011
[2,1,1,2,2] => 10111010
[2,1,1,3,1] => 10111001
[2,1,1,4] => 10111000
[2,1,2,1,1,1] => 10110111
[2,1,2,1,2] => 10110110
[2,1,2,2,1] => 10110101
[2,1,2,3] => 10110100
[2,1,3,1,1] => 10110011
[2,1,3,2] => 10110010
[2,1,4,1] => 10110001
[2,1,5] => 10110000
[2,2,1,1,1,1] => 10101111
[2,2,1,1,2] => 10101110
[2,2,1,2,1] => 10101101
[2,2,1,3] => 10101100
[2,2,2,1,1] => 10101011
[2,2,2,2] => 10101010
[2,2,3,1] => 10101001
[2,2,4] => 10101000
[2,3,1,1,1] => 10100111
[2,3,1,2] => 10100110
[2,3,2,1] => 10100101
[2,3,3] => 10100100
[2,4,1,1] => 10100011
[2,4,2] => 10100010
[2,5,1] => 10100001
[2,6] => 10100000
[3,1,1,1,1,1] => 10011111
[3,1,1,1,2] => 10011110
[3,1,1,2,1] => 10011101
[3,1,1,3] => 10011100
[3,1,2,1,1] => 10011011
[3,1,2,2] => 10011010
[3,1,3,1] => 10011001
[3,1,4] => 10011000
[3,2,1,1,1] => 10010111
[3,2,1,2] => 10010110
[3,2,2,1] => 10010101
[3,2,3] => 10010100
[3,3,1,1] => 10010011
[3,3,2] => 10010010
[3,4,1] => 10010001
[3,5] => 10010000
[4,1,1,1,1] => 10001111
[4,1,1,2] => 10001110
[4,1,2,1] => 10001101
[4,1,3] => 10001100
[4,2,1,1] => 10001011
[4,2,2] => 10001010
[4,3,1] => 10001001
[4,4] => 10001000
[5,1,1,1] => 10000111
[5,1,2] => 10000110
[5,2,1] => 10000101
[5,3] => 10000100
[6,1,1] => 10000011
[6,2] => 10000010
[7,1] => 10000001
[8] => 10000000
[1,1,1,1,1,1,1,1,1] => 111111111
[1,1,1,1,1,1,1,2] => 111111110
[1,1,1,1,1,1,2,1] => 111111101
[1,1,1,1,1,1,3] => 111111100
[1,1,1,1,1,2,1,1] => 111111011
[1,1,1,1,1,2,2] => 111111010
[1,1,1,1,1,3,1] => 111111001
[1,1,1,1,1,4] => 111111000
[1,1,1,1,2,1,1,1] => 111110111
[1,1,1,1,2,1,2] => 111110110
[1,1,1,1,2,2,1] => 111110101
[1,1,1,1,2,3] => 111110100
[1,1,1,1,3,1,1] => 111110011
[1,1,1,1,3,2] => 111110010
[1,1,1,1,4,1] => 111110001
[1,1,1,1,5] => 111110000
[1,1,1,2,1,1,1,1] => 111101111
[1,1,1,2,1,1,2] => 111101110
[1,1,1,2,1,2,1] => 111101101
[1,1,1,2,1,3] => 111101100
[1,1,1,2,2,1,1] => 111101011
[1,1,1,2,2,2] => 111101010
[1,1,1,2,3,1] => 111101001
[1,1,1,2,4] => 111101000
[1,1,1,3,1,1,1] => 111100111
[1,1,1,3,1,2] => 111100110
[1,1,1,3,2,1] => 111100101
[1,1,1,3,3] => 111100100
[1,1,1,4,1,1] => 111100011
[1,1,1,4,2] => 111100010
[1,1,1,5,1] => 111100001
[1,1,1,6] => 111100000
[1,1,2,1,1,1,1,1] => 111011111
[1,1,2,1,1,1,2] => 111011110
[1,1,2,1,1,2,1] => 111011101
[1,1,2,1,1,3] => 111011100
[1,1,2,1,2,1,1] => 111011011
[1,1,2,1,2,2] => 111011010
[1,1,2,1,3,1] => 111011001
[1,1,2,1,4] => 111011000
[1,1,2,2,1,1,1] => 111010111
[1,1,2,2,1,2] => 111010110
[1,1,2,2,2,1] => 111010101
[1,1,2,2,3] => 111010100
[1,1,2,3,1,1] => 111010011
[1,1,2,3,2] => 111010010
[1,1,2,4,1] => 111010001
[1,1,2,5] => 111010000
[1,1,3,1,1,1,1] => 111001111
[1,1,3,1,1,2] => 111001110
[1,1,3,1,2,1] => 111001101
[1,1,3,1,3] => 111001100
[1,1,3,2,1,1] => 111001011
[1,1,3,2,2] => 111001010
[1,1,3,3,1] => 111001001
[1,1,3,4] => 111001000
[1,1,4,1,1,1] => 111000111
[1,1,4,1,2] => 111000110
[1,1,4,2,1] => 111000101
[1,1,4,3] => 111000100
[1,1,5,1,1] => 111000011
[1,1,5,2] => 111000010
[1,1,6,1] => 111000001
[1,1,7] => 111000000
[1,2,1,1,1,1,1,1] => 110111111
[1,2,1,1,1,1,2] => 110111110
[1,2,1,1,1,2,1] => 110111101
[1,2,1,1,1,3] => 110111100
[1,2,1,1,2,1,1] => 110111011
[1,2,1,1,2,2] => 110111010
[1,2,1,1,3,1] => 110111001
[1,2,1,1,4] => 110111000
[1,2,1,2,1,1,1] => 110110111
[1,2,1,2,1,2] => 110110110
[1,2,1,2,2,1] => 110110101
[1,2,1,2,3] => 110110100
[1,2,1,3,1,1] => 110110011
[1,2,1,3,2] => 110110010
[1,2,1,4,1] => 110110001
[1,2,1,5] => 110110000
[1,2,2,1,1,1,1] => 110101111
[1,2,2,1,1,2] => 110101110
[1,2,2,1,2,1] => 110101101
[1,2,2,1,3] => 110101100
[1,2,2,2,1,1] => 110101011
[1,2,2,2,2] => 110101010
[1,2,2,3,1] => 110101001
[1,2,2,4] => 110101000
[1,2,3,1,1,1] => 110100111
[1,2,3,1,2] => 110100110
[1,2,3,2,1] => 110100101
[1,2,3,3] => 110100100
[1,2,4,1,1] => 110100011
[1,2,4,2] => 110100010
[1,2,5,1] => 110100001
[1,2,6] => 110100000
[1,3,1,1,1,1,1] => 110011111
[1,3,1,1,1,2] => 110011110
[1,3,1,1,2,1] => 110011101
[1,3,1,1,3] => 110011100
[1,3,1,2,1,1] => 110011011
[1,3,1,2,2] => 110011010
[1,3,1,3,1] => 110011001
[1,3,1,4] => 110011000
[1,3,2,1,1,1] => 110010111
[1,3,2,1,2] => 110010110
[1,3,2,2,1] => 110010101
[1,3,2,3] => 110010100
[1,3,3,1,1] => 110010011
[1,3,3,2] => 110010010
[1,3,4,1] => 110010001
[1,3,5] => 110010000
[1,4,1,1,1,1] => 110001111
[1,4,1,1,2] => 110001110
[1,4,1,2,1] => 110001101
[1,4,1,3] => 110001100
[1,4,2,1,1] => 110001011
[1,4,2,2] => 110001010
[1,4,3,1] => 110001001
[1,4,4] => 110001000
[1,5,1,1,1] => 110000111
[1,5,1,2] => 110000110
[1,5,2,1] => 110000101
[1,5,3] => 110000100
[1,6,1,1] => 110000011
[1,6,2] => 110000010
[1,7,1] => 110000001
[1,8] => 110000000
[2,1,1,1,1,1,1,1] => 101111111
[2,1,1,1,1,1,2] => 101111110
[2,1,1,1,1,2,1] => 101111101
[2,1,1,1,1,3] => 101111100
[2,1,1,1,2,1,1] => 101111011
[2,1,1,1,2,2] => 101111010
[2,1,1,1,3,1] => 101111001
[2,1,1,1,4] => 101111000
[2,1,1,2,1,1,1] => 101110111
[2,1,1,2,1,2] => 101110110
[2,1,1,2,2,1] => 101110101
[2,1,1,2,3] => 101110100
[2,1,1,3,1,1] => 101110011
[2,1,1,3,2] => 101110010
[2,1,1,4,1] => 101110001
[2,1,1,5] => 101110000
[2,1,2,1,1,1,1] => 101101111
[2,1,2,1,1,2] => 101101110
[2,1,2,1,2,1] => 101101101
[2,1,2,1,3] => 101101100
[2,1,2,2,1,1] => 101101011
[2,1,2,2,2] => 101101010
[2,1,2,3,1] => 101101001
[2,1,2,4] => 101101000
[2,1,3,1,1,1] => 101100111
[2,1,3,1,2] => 101100110
[2,1,3,2,1] => 101100101
[2,1,3,3] => 101100100
[2,1,4,1,1] => 101100011
[2,1,4,2] => 101100010
[2,1,5,1] => 101100001
[2,1,6] => 101100000
[2,2,1,1,1,1,1] => 101011111
[2,2,1,1,1,2] => 101011110
[2,2,1,1,2,1] => 101011101
[2,2,1,1,3] => 101011100
[2,2,1,2,1,1] => 101011011
[2,2,1,2,2] => 101011010
[2,2,1,3,1] => 101011001
[2,2,1,4] => 101011000
[2,2,2,1,1,1] => 101010111
[2,2,2,1,2] => 101010110
[2,2,2,2,1] => 101010101
[2,2,2,3] => 101010100
[2,2,3,1,1] => 101010011
[2,2,3,2] => 101010010
[2,2,4,1] => 101010001
[2,2,5] => 101010000
[2,3,1,1,1,1] => 101001111
[2,3,1,1,2] => 101001110
[2,3,1,2,1] => 101001101
[2,3,1,3] => 101001100
[2,3,2,1,1] => 101001011
[2,3,2,2] => 101001010
[2,3,3,1] => 101001001
[2,3,4] => 101001000
[2,4,1,1,1] => 101000111
[2,4,1,2] => 101000110
[2,4,2,1] => 101000101
[2,4,3] => 101000100
[2,5,1,1] => 101000011
[2,5,2] => 101000010
[2,6,1] => 101000001
[2,7] => 101000000
[3,1,1,1,1,1,1] => 100111111
[3,1,1,1,1,2] => 100111110
[3,1,1,1,2,1] => 100111101
[3,1,1,1,3] => 100111100
[3,1,1,2,1,1] => 100111011
[3,1,1,2,2] => 100111010
[3,1,1,3,1] => 100111001
[3,1,1,4] => 100111000
[3,1,2,1,1,1] => 100110111
[3,1,2,1,2] => 100110110
[3,1,2,2,1] => 100110101
[3,1,2,3] => 100110100
[3,1,3,1,1] => 100110011
[3,1,3,2] => 100110010
[3,1,4,1] => 100110001
[3,1,5] => 100110000
[3,2,1,1,1,1] => 100101111
[3,2,1,1,2] => 100101110
[3,2,1,2,1] => 100101101
[3,2,1,3] => 100101100
[3,2,2,1,1] => 100101011
[3,2,2,2] => 100101010
[3,2,3,1] => 100101001
[3,2,4] => 100101000
[3,3,1,1,1] => 100100111
[3,3,1,2] => 100100110
[3,3,2,1] => 100100101
[3,3,3] => 100100100
[3,4,1,1] => 100100011
[3,4,2] => 100100010
[3,5,1] => 100100001
[3,6] => 100100000
[4,1,1,1,1,1] => 100011111
[4,1,1,1,2] => 100011110
[4,1,1,2,1] => 100011101
[4,1,1,3] => 100011100
[4,1,2,1,1] => 100011011
[4,1,2,2] => 100011010
[4,1,3,1] => 100011001
[4,1,4] => 100011000
[4,2,1,1,1] => 100010111
[4,2,1,2] => 100010110
[4,2,2,1] => 100010101
[4,2,3] => 100010100
[4,3,1,1] => 100010011
[4,3,2] => 100010010
[4,4,1] => 100010001
[4,5] => 100010000
[5,1,1,1,1] => 100001111
[5,1,1,2] => 100001110
[5,1,2,1] => 100001101
[5,1,3] => 100001100
[5,2,1,1] => 100001011
[5,2,2] => 100001010
[5,3,1] => 100001001
[5,4] => 100001000
[6,1,1,1] => 100000111
[6,1,2] => 100000110
[6,2,1] => 100000101
[6,3] => 100000100
[7,1,1] => 100000011
[7,2] => 100000010
[8,1] => 100000001
[9] => 100000000
[1,1,1,1,1,1,1,1,1,1] => 1111111111
[1,1,1,1,1,1,1,1,2] => 1111111110
[1,1,1,1,1,1,1,2,1] => 1111111101
[1,1,1,1,1,1,1,3] => 1111111100
[1,1,1,1,1,1,2,1,1] => 1111111011
[1,1,1,1,1,1,2,2] => 1111111010
[1,1,1,1,1,1,3,1] => 1111111001
[1,1,1,1,1,1,4] => 1111111000
[1,1,1,1,1,2,1,1,1] => 1111110111
[1,1,1,1,1,2,1,2] => 1111110110
[1,1,1,1,1,2,2,1] => 1111110101
[1,1,1,1,1,2,3] => 1111110100
[1,1,1,1,1,3,1,1] => 1111110011
[1,1,1,1,1,3,2] => 1111110010
[1,1,1,1,1,4,1] => 1111110001
[1,1,1,1,1,5] => 1111110000
[1,1,1,1,2,1,1,1,1] => 1111101111
[1,1,1,1,2,1,1,2] => 1111101110
[1,1,1,1,2,1,2,1] => 1111101101
[1,1,1,1,2,1,3] => 1111101100
[1,1,1,1,2,2,1,1] => 1111101011
[1,1,1,1,2,2,2] => 1111101010
[1,1,1,1,2,3,1] => 1111101001
[1,1,1,1,2,4] => 1111101000
[1,1,1,1,3,1,1,1] => 1111100111
[1,1,1,1,3,1,2] => 1111100110
[1,1,1,1,3,2,1] => 1111100101
[1,1,1,1,3,3] => 1111100100
[1,1,1,1,4,1,1] => 1111100011
[1,1,1,1,4,2] => 1111100010
[1,1,1,1,5,1] => 1111100001
[1,1,1,1,6] => 1111100000
[1,1,1,2,1,1,1,1,1] => 1111011111
[1,1,1,2,1,1,1,2] => 1111011110
[1,1,1,2,1,1,2,1] => 1111011101
[1,1,1,2,1,1,3] => 1111011100
[1,1,1,2,1,2,1,1] => 1111011011
[1,1,1,2,1,2,2] => 1111011010
[1,1,1,2,1,3,1] => 1111011001
[1,1,1,2,1,4] => 1111011000
[1,1,1,2,2,1,1,1] => 1111010111
[1,1,1,2,2,1,2] => 1111010110
[1,1,1,2,2,2,1] => 1111010101
[1,1,1,2,2,3] => 1111010100
[1,1,1,2,3,1,1] => 1111010011
[1,1,1,2,3,2] => 1111010010
[1,1,1,2,4,1] => 1111010001
[1,1,1,2,5] => 1111010000
[1,1,1,3,1,1,1,1] => 1111001111
[1,1,1,3,1,1,2] => 1111001110
[1,1,1,3,1,2,1] => 1111001101
[1,1,1,3,1,3] => 1111001100
[1,1,1,3,2,1,1] => 1111001011
[1,1,1,3,2,2] => 1111001010
[1,1,1,3,3,1] => 1111001001
[1,1,1,3,4] => 1111001000
[1,1,1,4,1,1,1] => 1111000111
[1,1,1,4,1,2] => 1111000110
[1,1,1,4,2,1] => 1111000101
[1,1,1,4,3] => 1111000100
[1,1,1,5,1,1] => 1111000011
[1,1,1,5,2] => 1111000010
[1,1,1,6,1] => 1111000001
[1,1,1,7] => 1111000000
[1,1,2,1,1,1,1,1,1] => 1110111111
[1,1,2,1,1,1,1,2] => 1110111110
[1,1,2,1,1,1,2,1] => 1110111101
[1,1,2,1,1,1,3] => 1110111100
[1,1,2,1,1,2,1,1] => 1110111011
[1,1,2,1,1,2,2] => 1110111010
[1,1,2,1,1,3,1] => 1110111001
[1,1,2,1,1,4] => 1110111000
[1,1,2,1,2,1,1,1] => 1110110111
[1,1,2,1,2,1,2] => 1110110110
[1,1,2,1,2,2,1] => 1110110101
[1,1,2,1,2,3] => 1110110100
[1,1,2,1,3,1,1] => 1110110011
[1,1,2,1,3,2] => 1110110010
[1,1,2,1,4,1] => 1110110001
[1,1,2,1,5] => 1110110000
[1,1,2,2,1,1,1,1] => 1110101111
[1,1,2,2,1,1,2] => 1110101110
[1,1,2,2,1,2,1] => 1110101101
[1,1,2,2,1,3] => 1110101100
[1,1,2,2,2,1,1] => 1110101011
[1,1,2,2,2,2] => 1110101010
[1,1,2,2,3,1] => 1110101001
[1,1,2,2,4] => 1110101000
[1,1,2,3,1,1,1] => 1110100111
[1,1,2,3,1,2] => 1110100110
[1,1,2,3,2,1] => 1110100101
[1,1,2,3,3] => 1110100100
[1,1,2,4,1,1] => 1110100011
[1,1,2,4,2] => 1110100010
[1,1,2,5,1] => 1110100001
[1,1,2,6] => 1110100000
[1,1,3,1,1,1,1,1] => 1110011111
[1,1,3,1,1,1,2] => 1110011110
[1,1,3,1,1,2,1] => 1110011101
[1,1,3,1,1,3] => 1110011100
[1,1,3,1,2,1,1] => 1110011011
[1,1,3,1,2,2] => 1110011010
[1,1,3,1,3,1] => 1110011001
[1,1,3,1,4] => 1110011000
[1,1,3,2,1,1,1] => 1110010111
[1,1,3,2,1,2] => 1110010110
[1,1,3,2,2,1] => 1110010101
[1,1,3,2,3] => 1110010100
[1,1,3,3,1,1] => 1110010011
[1,1,3,3,2] => 1110010010
[1,1,3,4,1] => 1110010001
[1,1,3,5] => 1110010000
[1,1,4,1,1,1,1] => 1110001111
[1,1,4,1,1,2] => 1110001110
[1,1,4,1,2,1] => 1110001101
[1,1,4,1,3] => 1110001100
[1,1,4,2,1,1] => 1110001011
[1,1,4,2,2] => 1110001010
[1,1,4,3,1] => 1110001001
[1,1,4,4] => 1110001000
[1,1,5,1,1,1] => 1110000111
[1,1,5,1,2] => 1110000110
[1,1,5,2,1] => 1110000101
[1,1,5,3] => 1110000100
[1,1,6,1,1] => 1110000011
[1,1,6,2] => 1110000010
[1,1,7,1] => 1110000001
[1,1,8] => 1110000000
[1,2,1,1,1,1,1,1,1] => 1101111111
[1,2,1,1,1,1,1,2] => 1101111110
[1,2,1,1,1,1,2,1] => 1101111101
[1,2,1,1,1,1,3] => 1101111100
[1,2,1,1,1,2,1,1] => 1101111011
[1,2,1,1,1,2,2] => 1101111010
[1,2,1,1,1,3,1] => 1101111001
[1,2,1,1,1,4] => 1101111000
[1,2,1,1,2,1,1,1] => 1101110111
[1,2,1,1,2,1,2] => 1101110110
[1,2,1,1,2,2,1] => 1101110101
[1,2,1,1,2,3] => 1101110100
[1,2,1,1,3,1,1] => 1101110011
[1,2,1,1,3,2] => 1101110010
[1,2,1,1,4,1] => 1101110001
[1,2,1,1,5] => 1101110000
[1,2,1,2,1,1,1,1] => 1101101111
[1,2,1,2,1,1,2] => 1101101110
[1,2,1,2,1,2,1] => 1101101101
[1,2,1,2,1,3] => 1101101100
[1,2,1,2,2,1,1] => 1101101011
[1,2,1,2,2,2] => 1101101010
[1,2,1,2,3,1] => 1101101001
[1,2,1,2,4] => 1101101000
[1,2,1,3,1,1,1] => 1101100111
[1,2,1,3,1,2] => 1101100110
[1,2,1,3,2,1] => 1101100101
[1,2,1,3,3] => 1101100100
[1,2,1,4,1,1] => 1101100011
[1,2,1,4,2] => 1101100010
[1,2,1,5,1] => 1101100001
[1,2,1,6] => 1101100000
[1,2,2,1,1,1,1,1] => 1101011111
[1,2,2,1,1,1,2] => 1101011110
[1,2,2,1,1,2,1] => 1101011101
[1,2,2,1,1,3] => 1101011100
[1,2,2,1,2,1,1] => 1101011011
[1,2,2,1,2,2] => 1101011010
[1,2,2,1,3,1] => 1101011001
[1,2,2,1,4] => 1101011000
[1,2,2,2,1,1,1] => 1101010111
[1,2,2,2,1,2] => 1101010110
[1,2,2,2,2,1] => 1101010101
[1,2,2,2,3] => 1101010100
[1,2,2,3,1,1] => 1101010011
[1,2,2,3,2] => 1101010010
[1,2,2,4,1] => 1101010001
[1,2,2,5] => 1101010000
[1,2,3,1,1,1,1] => 1101001111
[1,2,3,1,1,2] => 1101001110
[1,2,3,1,2,1] => 1101001101
[1,2,3,1,3] => 1101001100
[1,2,3,2,1,1] => 1101001011
[1,2,3,2,2] => 1101001010
[1,2,3,3,1] => 1101001001
[1,2,3,4] => 1101001000
[1,2,4,1,1,1] => 1101000111
[1,2,4,1,2] => 1101000110
[1,2,4,2,1] => 1101000101
[1,2,4,3] => 1101000100
[1,2,5,1,1] => 1101000011
[1,2,5,2] => 1101000010
[1,2,6,1] => 1101000001
[1,2,7] => 1101000000
[1,3,1,1,1,1,1,1] => 1100111111
[1,3,1,1,1,1,2] => 1100111110
[1,3,1,1,1,2,1] => 1100111101
[1,3,1,1,1,3] => 1100111100
[1,3,1,1,2,1,1] => 1100111011
[1,3,1,1,2,2] => 1100111010
[1,3,1,1,3,1] => 1100111001
[1,3,1,1,4] => 1100111000
[1,3,1,2,1,1,1] => 1100110111
[1,3,1,2,1,2] => 1100110110
[1,3,1,2,2,1] => 1100110101
[1,3,1,2,3] => 1100110100
[1,3,1,3,1,1] => 1100110011
[1,3,1,3,2] => 1100110010
[1,3,1,4,1] => 1100110001
[1,3,1,5] => 1100110000
[1,3,2,1,1,1,1] => 1100101111
[1,3,2,1,1,2] => 1100101110
[1,3,2,1,2,1] => 1100101101
[1,3,2,1,3] => 1100101100
[1,3,2,2,1,1] => 1100101011
[1,3,2,2,2] => 1100101010
[1,3,2,3,1] => 1100101001
[1,3,2,4] => 1100101000
[1,3,3,1,1,1] => 1100100111
[1,3,3,1,2] => 1100100110
[1,3,3,2,1] => 1100100101
[1,3,3,3] => 1100100100
[1,3,4,1,1] => 1100100011
[1,3,4,2] => 1100100010
[1,3,5,1] => 1100100001
[1,3,6] => 1100100000
[1,4,1,1,1,1,1] => 1100011111
[1,4,1,1,1,2] => 1100011110
[1,4,1,1,2,1] => 1100011101
[1,4,1,1,3] => 1100011100
[1,4,1,2,1,1] => 1100011011
[1,4,1,2,2] => 1100011010
[1,4,1,3,1] => 1100011001
[1,4,1,4] => 1100011000
[1,4,2,1,1,1] => 1100010111
[1,4,2,1,2] => 1100010110
[1,4,2,2,1] => 1100010101
[1,4,2,3] => 1100010100
[1,4,3,1,1] => 1100010011
[1,4,3,2] => 1100010010
[1,4,4,1] => 1100010001
[1,4,5] => 1100010000
[1,5,1,1,1,1] => 1100001111
[1,5,1,1,2] => 1100001110
[1,5,1,2,1] => 1100001101
[1,5,1,3] => 1100001100
[1,5,2,1,1] => 1100001011
[1,5,2,2] => 1100001010
[1,5,3,1] => 1100001001
[1,5,4] => 1100001000
[1,6,1,1,1] => 1100000111
[1,6,1,2] => 1100000110
[1,6,2,1] => 1100000101
[1,6,3] => 1100000100
[1,7,1,1] => 1100000011
[1,7,2] => 1100000010
[1,8,1] => 1100000001
[1,9] => 1100000000
[2,1,1,1,1,1,1,1,1] => 1011111111
[2,1,1,1,1,1,1,2] => 1011111110
[2,1,1,1,1,1,2,1] => 1011111101
[2,1,1,1,1,1,3] => 1011111100
[2,1,1,1,1,2,1,1] => 1011111011
[2,1,1,1,1,2,2] => 1011111010
[2,1,1,1,1,3,1] => 1011111001
[2,1,1,1,1,4] => 1011111000
[2,1,1,1,2,1,1,1] => 1011110111
[2,1,1,1,2,1,2] => 1011110110
[2,1,1,1,2,2,1] => 1011110101
[2,1,1,1,2,3] => 1011110100
[2,1,1,1,3,1,1] => 1011110011
[2,1,1,1,3,2] => 1011110010
[2,1,1,1,4,1] => 1011110001
[2,1,1,1,5] => 1011110000
[2,1,1,2,1,1,1,1] => 1011101111
[2,1,1,2,1,1,2] => 1011101110
[2,1,1,2,1,2,1] => 1011101101
[2,1,1,2,1,3] => 1011101100
[2,1,1,2,2,1,1] => 1011101011
[2,1,1,2,2,2] => 1011101010
[2,1,1,2,3,1] => 1011101001
[2,1,1,2,4] => 1011101000
[2,1,1,3,1,1,1] => 1011100111
[2,1,1,3,1,2] => 1011100110
[2,1,1,3,2,1] => 1011100101
[2,1,1,3,3] => 1011100100
[2,1,1,4,1,1] => 1011100011
[2,1,1,4,2] => 1011100010
[2,1,1,5,1] => 1011100001
[2,1,1,6] => 1011100000
[2,1,2,1,1,1,1,1] => 1011011111
[2,1,2,1,1,1,2] => 1011011110
[2,1,2,1,1,2,1] => 1011011101
[2,1,2,1,1,3] => 1011011100
[2,1,2,1,2,1,1] => 1011011011
[2,1,2,1,2,2] => 1011011010
[2,1,2,1,3,1] => 1011011001
[2,1,2,1,4] => 1011011000
[2,1,2,2,1,1,1] => 1011010111
[2,1,2,2,1,2] => 1011010110
[2,1,2,2,2,1] => 1011010101
[2,1,2,2,3] => 1011010100
[2,1,2,3,1,1] => 1011010011
[2,1,2,3,2] => 1011010010
[2,1,2,4,1] => 1011010001
[2,1,2,5] => 1011010000
[2,1,3,1,1,1,1] => 1011001111
[2,1,3,1,1,2] => 1011001110
[2,1,3,1,2,1] => 1011001101
[2,1,3,1,3] => 1011001100
[2,1,3,2,1,1] => 1011001011
[2,1,3,2,2] => 1011001010
[2,1,3,3,1] => 1011001001
[2,1,3,4] => 1011001000
[2,1,4,1,1,1] => 1011000111
[2,1,4,1,2] => 1011000110
[2,1,4,2,1] => 1011000101
[2,1,4,3] => 1011000100
[2,1,5,1,1] => 1011000011
[2,1,5,2] => 1011000010
[2,1,6,1] => 1011000001
[2,1,7] => 1011000000
[2,2,1,1,1,1,1,1] => 1010111111
[2,2,1,1,1,1,2] => 1010111110
[2,2,1,1,1,2,1] => 1010111101
[2,2,1,1,1,3] => 1010111100
[2,2,1,1,2,1,1] => 1010111011
[2,2,1,1,2,2] => 1010111010
[2,2,1,1,3,1] => 1010111001
[2,2,1,1,4] => 1010111000
[2,2,1,2,1,1,1] => 1010110111
[2,2,1,2,1,2] => 1010110110
[2,2,1,2,2,1] => 1010110101
[2,2,1,2,3] => 1010110100
[2,2,1,3,1,1] => 1010110011
[2,2,1,3,2] => 1010110010
[2,2,1,4,1] => 1010110001
[2,2,1,5] => 1010110000
[2,2,2,1,1,1,1] => 1010101111
[2,2,2,1,1,2] => 1010101110
[2,2,2,1,2,1] => 1010101101
[2,2,2,1,3] => 1010101100
[2,2,2,2,1,1] => 1010101011
[2,2,2,2,2] => 1010101010
[2,2,2,3,1] => 1010101001
[2,2,2,4] => 1010101000
[2,2,3,1,1,1] => 1010100111
[2,2,3,1,2] => 1010100110
[2,2,3,2,1] => 1010100101
[2,2,3,3] => 1010100100
[2,2,4,1,1] => 1010100011
[2,2,4,2] => 1010100010
[2,2,5,1] => 1010100001
[2,2,6] => 1010100000
[2,3,1,1,1,1,1] => 1010011111
[2,3,1,1,1,2] => 1010011110
[2,3,1,1,2,1] => 1010011101
[2,3,1,1,3] => 1010011100
[2,3,1,2,1,1] => 1010011011
[2,3,1,2,2] => 1010011010
[2,3,1,3,1] => 1010011001
[2,3,1,4] => 1010011000
[2,3,2,1,1,1] => 1010010111
[2,3,2,1,2] => 1010010110
[2,3,2,2,1] => 1010010101
[2,3,2,3] => 1010010100
[2,3,3,1,1] => 1010010011
[2,3,3,2] => 1010010010
[2,3,4,1] => 1010010001
[2,3,5] => 1010010000
[2,4,1,1,1,1] => 1010001111
[2,4,1,1,2] => 1010001110
[2,4,1,2,1] => 1010001101
[2,4,1,3] => 1010001100
[2,4,2,1,1] => 1010001011
[2,4,2,2] => 1010001010
[2,4,3,1] => 1010001001
[2,4,4] => 1010001000
[2,5,1,1,1] => 1010000111
[2,5,1,2] => 1010000110
[2,5,2,1] => 1010000101
[2,5,3] => 1010000100
[2,6,1,1] => 1010000011
[2,6,2] => 1010000010
[2,7,1] => 1010000001
[2,8] => 1010000000
[3,1,1,1,1,1,1,1] => 1001111111
[3,1,1,1,1,1,2] => 1001111110
[3,1,1,1,1,2,1] => 1001111101
[3,1,1,1,1,3] => 1001111100
[3,1,1,1,2,1,1] => 1001111011
[3,1,1,1,2,2] => 1001111010
[3,1,1,1,3,1] => 1001111001
[3,1,1,1,4] => 1001111000
[3,1,1,2,1,1,1] => 1001110111
[3,1,1,2,1,2] => 1001110110
[3,1,1,2,2,1] => 1001110101
[3,1,1,2,3] => 1001110100
[3,1,1,3,1,1] => 1001110011
[3,1,1,3,2] => 1001110010
[3,1,1,4,1] => 1001110001
[3,1,1,5] => 1001110000
[3,1,2,1,1,1,1] => 1001101111
[3,1,2,1,1,2] => 1001101110
[3,1,2,1,2,1] => 1001101101
[3,1,2,1,3] => 1001101100
[3,1,2,2,1,1] => 1001101011
[3,1,2,2,2] => 1001101010
[3,1,2,3,1] => 1001101001
[3,1,2,4] => 1001101000
[3,1,3,1,1,1] => 1001100111
[3,1,3,1,2] => 1001100110
[3,1,3,2,1] => 1001100101
[3,1,3,3] => 1001100100
[3,1,4,1,1] => 1001100011
[3,1,4,2] => 1001100010
[3,1,5,1] => 1001100001
[3,1,6] => 1001100000
[3,2,1,1,1,1,1] => 1001011111
[3,2,1,1,1,2] => 1001011110
[3,2,1,1,2,1] => 1001011101
[3,2,1,1,3] => 1001011100
[3,2,1,2,1,1] => 1001011011
[3,2,1,2,2] => 1001011010
[3,2,1,3,1] => 1001011001
[3,2,1,4] => 1001011000
[3,2,2,1,1,1] => 1001010111
[3,2,2,1,2] => 1001010110
[3,2,2,2,1] => 1001010101
[3,2,2,3] => 1001010100
[3,2,3,1,1] => 1001010011
[3,2,3,2] => 1001010010
[3,2,4,1] => 1001010001
[3,2,5] => 1001010000
[3,3,1,1,1,1] => 1001001111
[3,3,1,1,2] => 1001001110
[3,3,1,2,1] => 1001001101
[3,3,1,3] => 1001001100
[3,3,2,1,1] => 1001001011
[3,3,2,2] => 1001001010
[3,3,3,1] => 1001001001
[3,3,4] => 1001001000
[3,4,1,1,1] => 1001000111
[3,4,1,2] => 1001000110
[3,4,2,1] => 1001000101
[3,4,3] => 1001000100
[3,5,1,1] => 1001000011
[3,5,2] => 1001000010
[3,6,1] => 1001000001
[3,7] => 1001000000
[4,1,1,1,1,1,1] => 1000111111
[4,1,1,1,1,2] => 1000111110
[4,1,1,1,2,1] => 1000111101
[4,1,1,1,3] => 1000111100
[4,1,1,2,1,1] => 1000111011
[4,1,1,2,2] => 1000111010
[4,1,1,3,1] => 1000111001
[4,1,1,4] => 1000111000
[4,1,2,1,1,1] => 1000110111
[4,1,2,1,2] => 1000110110
[4,1,2,2,1] => 1000110101
[4,1,2,3] => 1000110100
[4,1,3,1,1] => 1000110011
[4,1,3,2] => 1000110010
[4,1,4,1] => 1000110001
[4,1,5] => 1000110000
[4,2,1,1,1,1] => 1000101111
[4,2,1,1,2] => 1000101110
[4,2,1,2,1] => 1000101101
[4,2,1,3] => 1000101100
[4,2,2,1,1] => 1000101011
[4,2,2,2] => 1000101010
[4,2,3,1] => 1000101001
[4,2,4] => 1000101000
[4,3,1,1,1] => 1000100111
[4,3,1,2] => 1000100110
[4,3,2,1] => 1000100101
[4,3,3] => 1000100100
[4,4,1,1] => 1000100011
[4,4,2] => 1000100010
[4,5,1] => 1000100001
[4,6] => 1000100000
[5,1,1,1,1,1] => 1000011111
[5,1,1,1,2] => 1000011110
[5,1,1,2,1] => 1000011101
[5,1,1,3] => 1000011100
[5,1,2,1,1] => 1000011011
[5,1,2,2] => 1000011010
[5,1,3,1] => 1000011001
[5,1,4] => 1000011000
[5,2,1,1,1] => 1000010111
[5,2,1,2] => 1000010110
[5,2,2,1] => 1000010101
[5,2,3] => 1000010100
[5,3,1,1] => 1000010011
[5,3,2] => 1000010010
[5,4,1] => 1000010001
[5,5] => 1000010000
[6,1,1,1,1] => 1000001111
[6,1,1,2] => 1000001110
[6,1,2,1] => 1000001101
[6,1,3] => 1000001100
[6,2,1,1] => 1000001011
[6,2,2] => 1000001010
[6,3,1] => 1000001001
[6,4] => 1000001000
[7,1,1,1] => 1000000111
[7,1,2] => 1000000110
[7,2,1] => 1000000101
[7,3] => 1000000100
[8,1,1] => 1000000011
[8,2] => 1000000010
[9,1] => 1000000001
[10] => 1000000000
[5,5,1,1] => 100001000011
[1,1,5,5] => 111000010000
[] => 0
[10,1] => 10000000001
[1,10] => 11000000000
[1,8,1,1] => 11000000011
[1,7,2,1] => 11000000101
[1,6,3,1] => 11000001001
[1,5,4,1] => 11000010001
[1,4,5,1] => 11000100001
[1,3,6,1] => 11001000001
[1,2,7,1] => 11010000001
[1,1,8,1] => 11100000001
[2,1,1,1,1,1,1,1,1,1] => 10111111111
[1,1,1,1,1,1,1,1,1,2] => 11111111110
[2,9] => 10100000000
[1,1,1,1,1,1,1,1,3] => 11111111100
[1,1,1,1,1,1,1,1,2,1] => 11111111101
[11] => 10000000000
[3,1,1,1,1,1,1,1,1] => 10011111111
[9,2] => 10000000010
[1,1,6,6] => 11100000100000
[1,1,4,1,1,4] => 111000111000
[4,1,1,4,1,1] => 100011100011
[6,6,1,1] => 10000010000011
[1,1,7,7] => 1110000001000000
[1,1,5,1,1,5] => 11100001110000
[1,1,3,1,2,4] => 111001101000
[1,1,4,2,1,3] => 111000101100
[3,1,2,4,1,1] => 100110100011
[4,2,1,3,1,1] => 100010110011
[5,1,1,5,1,1] => 10000111000011
[7,7,1,1] => 1000000100000011
[1,1,8,8] => 111000000010000000
[1,1,6,1,1,6] => 1110000011100000
[1,1,4,1,2,5] => 11100011010000
[1,1,5,2,1,4] => 11100001011000
[1,1,2,1,3,4] => 111011001000
[1,1,3,1,1,1,1,3] => 111001111100
[1,1,4,3,1,2] => 111000100110
[2,2,4,4] => 101010001000
[2,1,3,4,1,1] => 101100100011
[3,1,1,1,1,3,1,1] => 100111110011
[4,1,2,5,1,1] => 10001101000011
[4,4,2,2] => 100010001010
[4,3,1,2,1,1] => 100010011011
[5,2,1,4,1,1] => 10000101100011
[6,1,1,6,1,1] => 1000001110000011
[8,8,1,1] => 100000001000000011
[1,1,9,9] => 11100000000100000000
[1,1,7,1,1,7] => 111000000111000000
[1,1,5,1,2,6] => 1110000110100000
[1,1,6,2,1,5] => 1110000010110000
[1,1,3,1,3,5] => 11100110010000
[1,1,4,1,1,1,1,4] => 11100011111000
[1,1,5,3,1,3] => 11100001001100
[1,1,1,1,4,4] => 111110001000
[1,1,2,1,2,1,1,3] => 111011011100
[1,1,3,2,2,3] => 111001010100
[1,1,3,1,1,2,1,2] => 111001110110
[1,1,4,4,1,1] => 111000100011
[2,2,3,1,1,3] => 101010011100
[2,1,2,1,1,3,1,1] => 101101110011
[3,1,3,5,1,1] => 10011001000011
[3,3,3,3] => 100100100100
[3,2,2,3,1,1] => 100101010011
[3,1,1,3,2,2] => 100111001010
[3,1,1,2,1,2,1,1] => 100111011011
[4,1,1,1,1,4,1,1] => 10001111100011
[5,1,2,6,1,1] => 1000011010000011
[4,4,1,1,1,1] => 100010001111
[5,3,1,3,1,1] => 10000100110011
[6,2,1,5,1,1] => 1000001011000011
[7,1,1,7,1,1] => 100000011100000011
[9,9,1,1] => 10000000010000000011
[1,1,10,10] => 1110000000001000000000
[1,1,8,1,1,8] => 11100000001110000000
[1,1,6,1,2,7] => 111000001101000000
[1,1,7,2,1,6] => 111000000101100000
[1,1,4,1,3,6] => 1110001100100000
[1,1,5,1,1,1,1,5] => 1110000111110000
[1,1,6,3,1,4] => 1110000010011000
[1,1,2,1,4,5] => 11101100010000
[1,1,3,1,2,1,1,4] => 11100110111000
[1,1,4,2,2,4] => 11100010101000
[1,1,4,1,1,2,1,3] => 11100011101100
[1,1,5,4,1,2] => 11100001000110
[2,2,5,5] => 10101000010000
[1,1,1,1,3,1,1,3] => 111110011100
[1,1,2,1,1,1,2,3] => 111011110100
[1,1,2,1,2,2,1,2] => 111011010110
[1,1,3,2,1,1,1,2] => 111001011110
[1,1,3,1,1,3,1,1] => 111001110011
[2,1,4,5,1,1] => 10110001000011
[2,2,2,1,2,3] => 101010110100
[2,2,3,2,1,2] => 101010010110
[2,1,1,2,3,3] => 101110100100
[2,1,1,1,2,3,1,1] => 101111010011
[2,1,2,3,2,2] => 101101001010
[2,1,2,2,1,2,1,1] => 101101011011
[3,1,2,1,1,4,1,1] => 10011011100011
[4,1,3,6,1,1] => 1000110010000011
[3,3,2,1,1,2] => 100100101110
[3,2,1,2,2,2] => 100101101010
[3,2,1,1,1,2,1,1] => 100101111011
[4,2,2,4,1,1] => 10001010100011
[3,1,1,3,1,1,1,1] => 100111001111
[4,1,1,2,1,3,1,1] => 10001110110011
[5,1,1,1,1,5,1,1] => 1000011111000011
[6,1,2,7,1,1] => 100000110100000011
[5,5,2,2] => 10000100001010
[5,4,1,2,1,1] => 10000100011011
[6,3,1,4,1,1] => 1000001001100011
[7,2,1,6,1,1] => 100000010110000011
[8,1,1,8,1,1] => 10000000111000000011
[10,10,1,1] => 1000000000100000000011
[3,1,1,1,1,1,1,2] => 10011111110
[2,2,1,1,1,1,1,2] => 10101111110
[2,1,2,1,1,1,1,2] => 10110111110
[2,1,1,2,1,1,1,2] => 10111011110
[2,1,1,1,2,1,1,2] => 10111101110
[2,1,1,1,1,2,1,2] => 10111110110
[2,1,1,1,1,1,2,2] => 10111111010
[2,1,1,1,1,1,1,3] => 10111111100
[2,1,7,1] => 10110000001
[1,1,1,1,6,1] => 11111000001
[1,2,1,1,5,1] => 11011100001
[1,3,1,1,4,1] => 11001110001
[1,4,1,1,3,1] => 11000111001
[1,5,1,1,2,1] => 11000011101
[1,6,1,1,1,1] => 11000001111
[1,7,1,2] => 11000000110
[9,1,1] => 10000000011
[2,7,1,1] => 10100000011
[3,6,1,1] => 10010000011
[4,5,1,1] => 10001000011
[5,4,1,1] => 10000100011
[6,3,1,1] => 10000010011
[7,2,1,1] => 10000001011
[8,1,1,1] => 10000000111
[1,1,1,8] => 11110000000
[1,1,2,7] => 11101000000
[1,1,3,6] => 11100100000
[1,1,4,5] => 11100010000
[1,1,5,4] => 11100001000
[1,1,6,3] => 11100000100
[1,1,7,2] => 11100000010
[1,1,9] => 11100000000
[1,1,1,1,1,1,1,1,1,1,1] => 11111111111
[1,2,1,1,1,1,1,1,1,1] => 11011111111
[2,1,1,1,1,1,1,1,2] => 10111111110
[1,1,1,1,1,2,1,1,1,1] => 11111101111
[1,1,1,1,2,1,1,1,1,1] => 11111011111
[1,1,1,1,1,1,1,2,1,1] => 11111111011
[2,1,1,1,2,1,1,1,1] => 10111101111
[1,1,1,1,1,1,2,1,1,1] => 11111110111
[1,1,1,1,1,1,2,1,1,2] => 111111101110
[1,1,1,1,1,1,1,1,2,2] => 111111111010
[2,2,1,1,2,1,1,2] => 101011101110
[2,2,1,1,1,1,2,2] => 101011111010
[2,1,1,2,2,1,1,2] => 101110101110
[1,1,2,2,2,1,1,2] => 111010101110
[2,1,1,2,1,1,2,2] => 101110111010
[1,1,2,2,1,1,2,2] => 111010111010
[1,1,1,1,3,2,1,2] => 111110010110
[1,1,2,1,1,1,1,1,1,2] => 111011111110
[1,1,2,1,1,2,2,2] => 111011101010
[3,3,1,1,2,2] => 100100111010
[1,1,1,1,2,1,1,1,1,2] => 111110111110
[1,1,1,1,2,2,2,2] => 111110101010
[3,2,2,2,1,2] => 100101010110
[2,1,1,1,2,2,1,2] => 101111010110
[1,1,1,1,2,1,2,3] => 111110110100
[3,2,1,1,1,1,1,2] => 100101111110
[2,1,1,1,1,1,1,1,1,2] => 101111111110
[2,1,1,1,1,2,2,2] => 101111101010
[2,2,2,1,1,1,1,2] => 101010111110
Download as text // json // pdf
Description
Return the composition as binary word, treating ones as separators.
Encoding a positive integer $i$ as the word $10\dots 0$ consisting of a one followed by $i-1$ zeros, the binary word of a composition $(i_1,\dots,i_k)$ is the concatenation of of words for $i_1,\dots,i_k$.
Properties
injectiveA map $\phi: A \rightarrow B$ is injective if $\phi(a) = \phi(b)$ implies $a=b$., gradedA map $\phi: A \rightarrow B$ is graded for graded sets $A$ and $B$ if $\operatorname{deg}(a) = \operatorname{deg}(a')$ implies $\operatorname{deg}(\phi(a)) = \operatorname{deg}(\phi(a'))$ for all $a, a' \in A$.
Code
def to_binary_word(w):
    return Words([0,1])(w.to_code())
Updated
May 12, 2019 at 17:22 by Christian Stump