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Why are we interested in square-free words?
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Problem
There is wikipedia page about square-free words, and there are a lot of theorems about these words, and examples of infinite square-free words.
I am wondering: why are we interested in these words?
Are there real-life applications of these words? Why are square-free words more useful to consider than other words?
I am wondering: why are we interested in these words?
Are there real-life applications of these words? Why are square-free words more useful to consider than other words?
Solution
Under related concepts on the wiki page for square-free we find the notion of cube-free words. An example of such words is the (Prouhet-)Thue-Morse sequence. Which has a very real-life application.
The sequence has been discovered independently many times, not always by professional research mathematicians; for example, Max Euwe, a chess grandmaster, who held the World Championship title from 1935 to 1937, and mathematics teacher, discovered it in 1929 in an application to chess: by using its cube-free property (see above), he showed how to circumvent a rule aimed at preventing infinitely protracted games by declaring repetition of moves a draw.
The sequence has been discovered independently many times, not always by professional research mathematicians; for example, Max Euwe, a chess grandmaster, who held the World Championship title from 1935 to 1937, and mathematics teacher, discovered it in 1929 in an application to chess: by using its cube-free property (see above), he showed how to circumvent a rule aimed at preventing infinitely protracted games by declaring repetition of moves a draw.
Context
StackExchange Computer Science Q#104664, answer score: 3
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