New results on pseudosquare avoidance
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We start by considering binary words containing the minimum possible numbers of squares and antisquares (where an antisquare is a word of the form x x), and we completely classify which possibilities can occur. We consider avoiding x p(x), where p is any permutation of the underlying alphabet, and x t(x), where t is any transformation of the underlying alphabet. Finally, we prove the existence of an infinite binary word simultaneously avoiding all occurrences of x h(x) for every nonerasing morphism h and all sufficiently large words x.
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