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Identifier
Mp00273: Binary words Gray previousBinary words
Images
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0100011011=>1100011011 0100010111=>1100010111 0100001111=>1100001111 0011010101=>1011010101 0011010011=>1011010011 0011001101=>1011001101 0011001011=>1011001011 0011000111=>1011000111 0010110101=>1010110101 0010110011=>1010110011 0010101101=>1010101101 0010101011=>1010101011 0010100111=>1010100111 0010011101=>1010011101 0010011011=>1010011011 0010010111=>1010010111 0010001111=>1010001111 0001110101=>1001110101 0001110011=>1001110011 0001101101=>1001101101 0001101011=>1001101011 0001100111=>1001100111 0001011101=>1001011101 0001011011=>1001011011 0001010111=>1001010111 0001001111=>1001001111 0000111101=>1000111101 0000111011=>1000111011 0000110111=>1000110111 0000101111=>1000101111 0000011111=>1000011111 10000000000=>00000000000 10000000010=>11000000010 10000000110=>00000000110 10000001110=>11000001110 10000011110=>00000011110 10000111110=>11000111110 10001111110=>00001111110 10011111110=>11011111110 10111111110=>00111111110 11111111110=>10111111110 01111111111=>01011111111 01111111101=>11111111101 01111111001=>01011111001 01111110001=>11111110001 01111100001=>01011100001 01111000001=>11111000001 01110000001=>01010000001 01100000001=>11100000001 01000000001=>01100000001 00000000001=>10000000001 11010101010=>10010101010 11010101000=>01010101000 11010101100=>10010101100 11010100100=>01010100100 11010110100=>10010110100 11010010100=>01010010100 11011010100=>10011010100 11001010100=>01001010100 11101010100=>10101010100 10101010100=>00101010100 101010101010=>111010101010 101010101100=>111010101100 101010110010=>111010110010 101010110100=>111010110100 101010111000=>111010111000 101011001010=>111011001010 101011001100=>111011001100 101011010010=>111011010010 101011010100=>111011010100 101011011000=>111011011000 101011100010=>111011100010 101011100100=>111011100100 101011101000=>111011101000 101011110000=>111011110000 101100101010=>111100101010 101100101100=>111100101100 101100110010=>111100110010 101100110100=>111100110100 101100111000=>111100111000 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100110001101=>110110001101 100110110111=>110110110111 100110110001=>110110110001 100110111101=>110110111101 100110100101=>110110100101 100001111111=>110001111111 100001111001=>110001111001 100001100111=>110001100111 100001100001=>110001100001 100001101101=>110001101101 100000011111=>110000011111 100000011001=>110000011001 100000000111=>110000000111 100000000001=>110000000001 100000001101=>110000001101 100000110111=>110000110111 100000110001=>110000110001 100000111101=>110000111101 100000100101=>110000100101 100011011111=>110011011111 100011011001=>110011011001 100011000111=>110011000111 100011000001=>110011000001 100011001101=>110011001101 100011110111=>110011110111 100011110001=>110011110001 100011111101=>110011111101 100011100101=>110011100101 100010010111=>110010010111 100010010001=>110010010001 100010011101=>110010011101 100010000101=>110010000101 100010110101=>110010110101 101101111111=>111101111111 101101111001=>111101111001 101101100111=>111101100111 101101100001=>111101100001 101101101101=>111101101101 101100011111=>111100011111 101100011001=>111100011001 101100000111=>111100000111 101100000001=>111100000001 101100001101=>111100001101 101100110111=>111100110111 101100110001=>111100110001 101100111101=>111100111101 101100100101=>111100100101 101111011111=>111111011111 101111011001=>111111011001 101111000111=>111111000111 101111000001=>111111000001 101111001101=>111111001101 101111110111=>111111110111 101111110001=>111111110001 101111111101=>111111111101 101111100101=>111111100101 101110010111=>111110010111 101110010001=>111110010001 101110011101=>111110011101 101110000101=>111110000101 101110110101=>111110110101 101001011111=>111001011111 101001011001=>111001011001 101001000111=>111001000111 101001000001=>111001000001 101001001101=>111001001101 101001110111=>111001110111 101001110001=>111001110001 101001111101=>111001111101 101001100101=>111001100101 101000010111=>111000010111 101000010001=>111000010001 101000011101=>111000011101 101000000101=>111000000101 101000110101=>111000110101 101011010111=>111011010111 101011010001=>111011010001 101011011101=>111011011101 101011000101=>111011000101 101011110101=>111011110101 101010010101=>111010010101
Description
The previous element in the Gray code for binary words.
Let $w$ be a binary word. If the number of ones in $w$ is odd, return the binary word obtained by flipping the first bit of $w$. If $w$ has only zeros, return the word with the final bit flipped. Otherwise, return the word obtained by flipping the bit after the first one.
References
Properties
bijective
Sage code
def mapping(w):
    if not w:
        return w
    w = list(w)
    if is_odd(w.count(1)):
        w[0] = 1 - w[0]
        return Word(w)
    try:
        i = w.index(1)
        w[i + 1] = 1 - w[i + 1]
        return Word(w)
    except ValueError:
        w[-1] = 1
        return Word(w)

Weight
51
Created
Dec 08, 2022 at 17:42 by Martin Rubey
Updated
Dec 08, 2022 at 17:42 by Martin Rubey