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Identifier
Mp00272: Binary words —Gray next⟶ Binary words
Images
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11010101101000=>10010101101000 11010101110000=>10010101110000 11010110010100=>10010110010100 11010110011000=>10010110011000 11010110100100=>10010110100100 11010110101000=>10010110101000 11010110110000=>10010110110000 11010111000100=>10010111000100 11010111001000=>10010111001000 11010111010000=>10010111010000 11010111100000=>10010111100000 11011001010100=>10011001010100 11011001011000=>10011001011000 11011001100100=>10011001100100 11011001101000=>10011001101000 11011001110000=>10011001110000 11011010010100=>10011010010100 11011010011000=>10011010011000 11011010100100=>10011010100100 11011010101000=>10011010101000 11011010110000=>10011010110000 11011011000100=>10011011000100 11011011001000=>10011011001000 11011011010000=>10011011010000 11011011100000=>10011011100000 11011100010100=>10011100010100 11011100011000=>10011100011000 11011100100100=>10011100100100 11011100101000=>10011100101000 11011100110000=>10011100110000 11011101000100=>10011101000100 11011101001000=>10011101001000 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1011010101010100=>0011010101010100 1011100101010100=>0011100101010100 1011101001010100=>0011101001010100 1011110001010100=>0011110001010100 1011110111000000=>0011110111000000 1011111010100000=>0011111010100000 1011111011000000=>0011111011000000 1011111100010000=>0011111100010000 1011111100100000=>0011111100100000 1011111101000000=>0011111101000000 1011111110000000=>0011111110000000 1101010101010100=>0101010101010100 1110010101010100=>0110010101010100 1110100101010100=>0110100101010100 1111000101010100=>0111000101010100 1111011100000010=>0111011100000010 1111101010000010=>0111101010000010 1111101100000010=>0111101100000010 1111110001000010=>0111110001000010 1111110010000010=>0111110010000010 1111110100000010=>0111110100000010 1111111000000010=>0111111000000010 101010101010101010=>111010101010101010 101010101010101100=>111010101010101100 101010101010110100=>111010101010110100 101010101011010100=>111010101011010100 101010101101010100=>111010101101010100 101010110101010100=>111010110101010100 101011010101010100=>111011010101010100 101101010101010100=>111101010101010100 110101010101010100=>100101010101010100 101010101010111000=>111010101010111000 101010101011100100=>111010101011100100 101010101110010100=>111010101110010100 101010111001010100=>111010111001010100 101011100101010100=>111011100101010100 101110010101010100=>111110010101010100 111001010101010100=>101001010101010100 111111110000000010=>101111110000000010 101111111100000000=>111111111100000000 111111101000000010=>101111101000000010 101111111010000000=>111111111010000000 111111100100000010=>101111100100000010 111111011000000010=>101111011000000010 101111111001000000=>111111111001000000 101111110110000000=>111111110110000000 10101010101010101010=>00101010101010101010 10101010101010101100=>00101010101010101100 10101010101010110100=>00101010101010110100 10101010101011010100=>00101010101011010100 10101010101101010100=>00101010101101010100 10101010110101010100=>00101010110101010100 10101011010101010100=>00101011010101010100 10101101010101010100=>00101101010101010100 10110101010101010100=>00110101010101010100 11010101010101010100=>01010101010101010100 11111111100000000010=>01111111100000000010 10111111111000000000=>00111111111000000000 11111111010000000010=>01111111010000000010 10111111110100000000=>00111111110100000000 1111111111000000000010=>1011111111000000000010 1011111111110000000000=>1111111111110000000000
click to show experimental identities (only identities of compositions of up to three maps are shown)
Description
The next element in the Gray code for binary words.
Let $w$ be a binary word. If the number of ones in $w$ is even, return the binary word obtained by flipping the first bit of $w$. If the only one in $w$ is the final bit, return the zero word. Otherwise, return the word obtained by flipping the bit after the first one.
References
[1] wikipedia:Gray code
Properties
bijective, graded
Sage code
def mapping(w):
    if not w:
        return w
    w = list(w)
    if is_even(w.count(1)):
        w[0] = 1 - w[0]
        return Word(w)
    i = w.index(1)
    n = len(w)
    if i + 1 == n:
        return Word([0]*n)
    w[i + 1] = 1 - w[i + 1]
    return Word(w)
Weight
40
Created
Dec 08, 2022 at 17:38 by Martin Rubey
Updated
Dec 08, 2022 at 17:38 by Martin Rubey