What is an example of an infinite word(superword) w such that if a nonempty word v belongs to L = {1,2,3}*, v^2 isn't a subword of w?For example if w = 123123123...123 and v = 123, v^2 = 123123 hence it's a subword of w, I can't seem to find a superword that fits the requirement.
Example of a superword w such that v^2 isn't its subword
formal languages
There is a dedicated page on square-free words on wikipedia here, with references. As you can see, there is an exemple of a square-free word on a three lettre alphabet.