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Identifier
Values
=>
0=>0 1=>0 00=>1 01=>0 10=>0 11=>1 000=>1 001=>0 010=>1 011=>0 100=>0 101=>1 110=>0 111=>1 0000=>2 0001=>1 0010=>1 0011=>0 0100=>1 0101=>0 0110=>2 0111=>1 1000=>1 1001=>2 1010=>0 1011=>1 1100=>0 1101=>1 1110=>1 1111=>2 00000=>2 00001=>1 00010=>1 00011=>0 00100=>2 00101=>1 00110=>1 00111=>0 01000=>1 01001=>0 01010=>2 01011=>1 01100=>1 01101=>0 01110=>2 01111=>1 10000=>1 10001=>2 10010=>0 10011=>1 10100=>1 10101=>2 10110=>0 10111=>1 11000=>0 11001=>1 11010=>1 11011=>2 11100=>0 11101=>1 11110=>1 11111=>2 000000=>3 000001=>2 000010=>2 000011=>1 000100=>2 000101=>1 000110=>1 000111=>0 001000=>2 001001=>1 001010=>1 001011=>0 001100=>3 001101=>2 001110=>2 001111=>1 010000=>2 010001=>1 010010=>3 010011=>2 010100=>1 010101=>0 010110=>2 010111=>1 011000=>1 011001=>0 011010=>2 011011=>1 011100=>2 011101=>1 011110=>3 011111=>2 100000=>2 100001=>3 100010=>1 100011=>2 100100=>1 100101=>2 100110=>0 100111=>1 101000=>1 101001=>2 101010=>0 101011=>1 101100=>2 101101=>3 101110=>1 101111=>2 110000=>1 110001=>2 110010=>2 110011=>3 110100=>0 110101=>1 110110=>1 110111=>2 111000=>0 111001=>1 111010=>1 111011=>2 111100=>1 111101=>2 111110=>2 111111=>3 0000000=>3 0000001=>2 0000010=>2 0000011=>1 0000100=>2 0000101=>1 0000110=>1 0000111=>0 0001000=>3 0001001=>2 0001010=>2 0001011=>1 0001100=>2 0001101=>1 0001110=>1 0001111=>0 0010000=>2 0010001=>1 0010010=>1 0010011=>0 0010100=>3 0010101=>2 0010110=>2 0010111=>1 0011000=>2 0011001=>1 0011010=>1 0011011=>0 0011100=>3 0011101=>2 0011110=>2 0011111=>1 0100000=>2 0100001=>1 0100010=>3 0100011=>2 0100100=>1 0100101=>0 0100110=>2 0100111=>1 0101000=>2 0101001=>1 0101010=>3 0101011=>2 0101100=>1 0101101=>0 0101110=>2 0101111=>1 0110000=>1 0110001=>0 0110010=>2 0110011=>1 0110100=>2 0110101=>1 0110110=>3 0110111=>2 0111000=>1 0111001=>0 0111010=>2 0111011=>1 0111100=>2 0111101=>1 0111110=>3 0111111=>2 1000000=>2 1000001=>3 1000010=>1 1000011=>2 1000100=>1 1000101=>2 1000110=>0 1000111=>1 1001000=>2 1001001=>3 1001010=>1 1001011=>2 1001100=>1 1001101=>2 1001110=>0 1001111=>1 1010000=>1 1010001=>2 1010010=>0 1010011=>1 1010100=>2 1010101=>3 1010110=>1 1010111=>2 1011000=>1 1011001=>2 1011010=>0 1011011=>1 1011100=>2 1011101=>3 1011110=>1 1011111=>2 1100000=>1 1100001=>2 1100010=>2 1100011=>3 1100100=>0 1100101=>1 1100110=>1 1100111=>2 1101000=>1 1101001=>2 1101010=>2 1101011=>3 1101100=>0 1101101=>1 1101110=>1 1101111=>2 1110000=>0 1110001=>1 1110010=>1 1110011=>2 1110100=>1 1110101=>2 1110110=>2 1110111=>3 1111000=>0 1111001=>1 1111010=>1 1111011=>2 1111100=>1 1111101=>2 1111110=>2 1111111=>3 00000000=>4 00000001=>3 00000010=>3 00000011=>2 00000100=>3 00000101=>2 00000110=>2 00000111=>1 00001000=>3 00001001=>2 00001010=>2 00001011=>1 00001100=>2 00001101=>1 00001110=>1 00001111=>0 00010000=>3 00010001=>2 00010010=>2 00010011=>1 00010100=>2 00010101=>1 00010110=>1 00010111=>0 00011000=>4 00011001=>3 00011010=>3 00011011=>2 00011100=>3 00011101=>2 00011110=>2 00011111=>1 00100000=>3 00100001=>2 00100010=>2 00100011=>1 00100100=>4 00100101=>3 00100110=>3 00100111=>2 00101000=>2 00101001=>1 00101010=>1 00101011=>0 00101100=>3 00101101=>2 00101110=>2 00101111=>1 00110000=>2 00110001=>1 00110010=>1 00110011=>0 00110100=>3 00110101=>2 00110110=>2 00110111=>1 00111000=>3 00111001=>2 00111010=>2 00111011=>1 00111100=>4 00111101=>3 00111110=>3 00111111=>2 01000000=>3 01000001=>2 01000010=>4 01000011=>3 01000100=>2 01000101=>1 01000110=>3 01000111=>2 01001000=>2 01001001=>1 01001010=>3 01001011=>2 01001100=>1 01001101=>0 01001110=>2 01001111=>1 01010000=>2 01010001=>1 01010010=>3 01010011=>2 01010100=>1 01010101=>0 01010110=>2 01010111=>1 01011000=>3 01011001=>2 01011010=>4 01011011=>3 01011100=>2 01011101=>1 01011110=>3 01011111=>2 01100000=>2 01100001=>1 01100010=>3 01100011=>2 01100100=>3 01100101=>2 01100110=>4 01100111=>3 01101000=>1 01101001=>0 01101010=>2 01101011=>1 01101100=>2 01101101=>1 01101110=>3 01101111=>2 01110000=>1 01110001=>0 01110010=>2 01110011=>1 01110100=>2 01110101=>1 01110110=>3 01110111=>2 01111000=>2 01111001=>1 01111010=>3 01111011=>2 01111100=>3 01111101=>2 01111110=>4 01111111=>3 10000000=>3 10000001=>4 10000010=>2 10000011=>3 10000100=>2 10000101=>3 10000110=>1 10000111=>2 10001000=>2 10001001=>3 10001010=>1 10001011=>2 10001100=>1 10001101=>2 10001110=>0 10001111=>1 10010000=>2 10010001=>3 10010010=>1 10010011=>2 10010100=>1 10010101=>2 10010110=>0 10010111=>1 10011000=>3 10011001=>4 10011010=>2 10011011=>3 10011100=>2 10011101=>3 10011110=>1 10011111=>2 10100000=>2 10100001=>3 10100010=>1 10100011=>2 10100100=>3 10100101=>4 10100110=>2 10100111=>3 10101000=>1 10101001=>2 10101010=>0 10101011=>1 10101100=>2 10101101=>3 10101110=>1 10101111=>2 10110000=>1 10110001=>2 10110010=>0 10110011=>1 10110100=>2 10110101=>3 10110110=>1 10110111=>2 10111000=>2 10111001=>3 10111010=>1 10111011=>2 10111100=>3 10111101=>4 10111110=>2 10111111=>3 11000000=>2 11000001=>3 11000010=>3 11000011=>4 11000100=>1 11000101=>2 11000110=>2 11000111=>3 11001000=>1 11001001=>2 11001010=>2 11001011=>3 11001100=>0 11001101=>1 11001110=>1 11001111=>2 11010000=>1 11010001=>2 11010010=>2 11010011=>3 11010100=>0 11010101=>1 11010110=>1 11010111=>2 11011000=>2 11011001=>3 11011010=>3 11011011=>4 11011100=>1 11011101=>2 11011110=>2 11011111=>3 11100000=>1 11100001=>2 11100010=>2 11100011=>3 11100100=>2 11100101=>3 11100110=>3 11100111=>4 11101000=>0 11101001=>1 11101010=>1 11101011=>2 11101100=>1 11101101=>2 11101110=>2 11101111=>3 11110000=>0 11110001=>1 11110010=>1 11110011=>2 11110100=>1 11110101=>2 11110110=>2 11110111=>3 11111000=>1 11111001=>2 11111010=>2 11111011=>3 11111100=>2 11111101=>3 11111110=>3 11111111=>4 000000000=>4 000000001=>3 000000010=>3 000000011=>2 000000100=>3 000000101=>2 000000110=>2 000000111=>1 000001000=>3 000001001=>2 000001010=>2 000001011=>1 000001100=>2 000001101=>1 000001110=>1 000001111=>0 000010000=>4 000010001=>3 000010010=>3 000010011=>2 000010100=>3 000010101=>2 000010110=>2 000010111=>1 000011000=>3 000011001=>2 000011010=>2 000011011=>1 000011100=>2 000011101=>1 000011110=>1 000011111=>0 000100000=>3 000100001=>2 000100010=>2 000100011=>1 000100100=>2 000100101=>1 000100110=>1 000100111=>0 000101000=>4 000101001=>3 000101010=>3 000101011=>2 000101100=>3 000101101=>2 000101110=>2 000101111=>1 000110000=>3 000110001=>2 000110010=>2 000110011=>1 000110100=>2 000110101=>1 000110110=>1 000110111=>0 000111000=>4 000111001=>3 000111010=>3 000111011=>2 000111100=>3 000111101=>2 000111110=>2 000111111=>1 001000000=>3 001000001=>2 001000010=>2 001000011=>1 001000100=>4 001000101=>3 001000110=>3 001000111=>2 001001000=>2 001001001=>1 001001010=>1 001001011=>0 001001100=>3 001001101=>2 001001110=>2 001001111=>1 001010000=>3 001010001=>2 001010010=>2 001010011=>1 001010100=>4 001010101=>3 001010110=>3 001010111=>2 001011000=>2 001011001=>1 001011010=>1 001011011=>0 001011100=>3 001011101=>2 001011110=>2 001011111=>1 001100000=>2 001100001=>1 001100010=>1 001100011=>0 001100100=>3 001100101=>2 001100110=>2 001100111=>1 001101000=>3 001101001=>2 001101010=>2 001101011=>1 001101100=>4 001101101=>3 001101110=>3 001101111=>2 001110000=>2 001110001=>1 001110010=>1 001110011=>0 001110100=>3 001110101=>2 001110110=>2 001110111=>1 001111000=>3 001111001=>2 001111010=>2 001111011=>1 001111100=>4 001111101=>3 001111110=>3 001111111=>2 010000000=>3 010000001=>2 010000010=>4 010000011=>3 010000100=>2 010000101=>1 010000110=>3 010000111=>2 010001000=>2 010001001=>1 010001010=>3 010001011=>2 010001100=>1 010001101=>0 010001110=>2 010001111=>1 010010000=>3 010010001=>2 010010010=>4 010010011=>3 010010100=>2 010010101=>1 010010110=>3 010010111=>2 010011000=>2 010011001=>1 010011010=>3 010011011=>2 010011100=>1 010011101=>0 010011110=>2 010011111=>1 010100000=>2 010100001=>1 010100010=>3 010100011=>2 010100100=>1 010100101=>0 010100110=>2 010100111=>1 010101000=>3 010101001=>2 010101010=>4 010101011=>3 010101100=>2 010101101=>1 010101110=>3 010101111=>2 010110000=>2 010110001=>1 010110010=>3 010110011=>2 010110100=>1 010110101=>0 010110110=>2 010110111=>1 010111000=>3 010111001=>2 010111010=>4 010111011=>3 010111100=>2 010111101=>1 010111110=>3 010111111=>2 011000000=>2 011000001=>1 011000010=>3 011000011=>2 011000100=>3 011000101=>2 011000110=>4 011000111=>3 011001000=>1 011001001=>0 011001010=>2 011001011=>1 011001100=>2 011001101=>1 011001110=>3 011001111=>2 011010000=>2 011010001=>1 011010010=>3 011010011=>2 011010100=>3 011010101=>2 011010110=>4 011010111=>3 011011000=>1 011011001=>0 011011010=>2 011011011=>1 011011100=>2 011011101=>1 011011110=>3 011011111=>2 011100000=>1 011100001=>0 011100010=>2 011100011=>1 011100100=>2 011100101=>1 011100110=>3 011100111=>2 011101000=>2 011101001=>1 011101010=>3 011101011=>2 011101100=>3 011101101=>2 011101110=>4 011101111=>3 011110000=>1 011110001=>0 011110010=>2 011110011=>1 011110100=>2 011110101=>1 011110110=>3 011110111=>2 011111000=>2 011111001=>1 011111010=>3 011111011=>2 011111100=>3 011111101=>2 011111110=>4 011111111=>3 100000000=>3 100000001=>4 100000010=>2 100000011=>3 100000100=>2 100000101=>3 100000110=>1 100000111=>2 100001000=>2 100001001=>3 100001010=>1 100001011=>2 100001100=>1 100001101=>2 100001110=>0 100001111=>1 100010000=>3 100010001=>4 100010010=>2 100010011=>3 100010100=>2 100010101=>3 100010110=>1 100010111=>2 100011000=>2 100011001=>3 100011010=>1 100011011=>2 100011100=>1 100011101=>2 100011110=>0 100011111=>1 100100000=>2 100100001=>3 100100010=>1 100100011=>2 100100100=>1 100100101=>2 100100110=>0 100100111=>1 100101000=>3 100101001=>4 100101010=>2 100101011=>3 100101100=>2 100101101=>3 100101110=>1 100101111=>2 100110000=>2 100110001=>3 100110010=>1 100110011=>2 100110100=>1 100110101=>2 100110110=>0 100110111=>1 100111000=>3 100111001=>4 100111010=>2 100111011=>3 100111100=>2 100111101=>3 100111110=>1 100111111=>2 101000000=>2 101000001=>3 101000010=>1 101000011=>2 101000100=>3 101000101=>4 101000110=>2 101000111=>3 101001000=>1 101001001=>2 101001010=>0 101001011=>1 101001100=>2 101001101=>3 101001110=>1 101001111=>2 101010000=>2 101010001=>3 101010010=>1 101010011=>2 101010100=>3 101010101=>4 101010110=>2 101010111=>3 101011000=>1 101011001=>2 101011010=>0 101011011=>1 101011100=>2 101011101=>3 101011110=>1 101011111=>2 101100000=>1 101100001=>2 101100010=>0 101100011=>1 101100100=>2 101100101=>3 101100110=>1 101100111=>2 101101000=>2 101101001=>3 101101010=>1 101101011=>2 101101100=>3 101101101=>4 101101110=>2 101101111=>3 101110000=>1 101110001=>2 101110010=>0 101110011=>1 101110100=>2 101110101=>3 101110110=>1 101110111=>2 101111000=>2 101111001=>3 101111010=>1 101111011=>2 101111100=>3 101111101=>4 101111110=>2 101111111=>3 110000000=>2 110000001=>3 110000010=>3 110000011=>4 110000100=>1 110000101=>2 110000110=>2 110000111=>3 110001000=>1 110001001=>2 110001010=>2 110001011=>3 110001100=>0 110001101=>1 110001110=>1 110001111=>2 110010000=>2 110010001=>3 110010010=>3 110010011=>4 110010100=>1 110010101=>2 110010110=>2 110010111=>3 110011000=>1 110011001=>2 110011010=>2 110011011=>3 110011100=>0 110011101=>1 110011110=>1 110011111=>2 110100000=>1 110100001=>2 110100010=>2 110100011=>3 110100100=>0 110100101=>1 110100110=>1 110100111=>2 110101000=>2 110101001=>3 110101010=>3 110101011=>4 110101100=>1 110101101=>2 110101110=>2 110101111=>3 110110000=>1 110110001=>2 110110010=>2 110110011=>3 110110100=>0 110110101=>1 110110110=>1 110110111=>2 110111000=>2 110111001=>3 110111010=>3 110111011=>4 110111100=>1 110111101=>2 110111110=>2 110111111=>3 111000000=>1 111000001=>2 111000010=>2 111000011=>3 111000100=>2 111000101=>3 111000110=>3 111000111=>4 111001000=>0 111001001=>1 111001010=>1 111001011=>2 111001100=>1 111001101=>2 111001110=>2 111001111=>3 111010000=>1 111010001=>2 111010010=>2 111010011=>3 111010100=>2 111010101=>3 111010110=>3 111010111=>4 111011000=>0 111011001=>1 111011010=>1 111011011=>2 111011100=>1 111011101=>2 111011110=>2 111011111=>3 111100000=>0 111100001=>1 111100010=>1 111100011=>2 111100100=>1 111100101=>2 111100110=>2 111100111=>3 111101000=>1 111101001=>2 111101010=>2 111101011=>3 111101100=>2 111101101=>3 111101110=>3 111101111=>4 111110000=>0 111110001=>1 111110010=>1 111110011=>2 111110100=>1 111110101=>2 111110110=>2 111110111=>3 111111000=>1 111111001=>2 111111010=>2 111111011=>3 111111100=>2 111111101=>3 111111110=>3 111111111=>4
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Description
The degree of symmetry of a binary word.
For a binary word $w$ of length $n$, this is the number of positions $i\leq n/2$ such that $w_i = w_{n+1-i}$.
Code
def statistic(D):
    result = sum(1 for a, b in zip(D, D[::-1]) if a == b)
    if is_even(len(D)):
        return result/2
    return (result-1)/2

Created
Mar 02, 2020 at 21:32 by Martin Rubey
Updated
Mar 02, 2020 at 21:32 by Martin Rubey