Lengths of extremal square-free ternary words
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A square-free word w over a fixed alphabet Σ is extremal if every word obtained from w by inserting a single letter from Σ (at any position) contains a square. Grytczuk et al. recently introduced the concept of extremal square-free word, and demonstrated that there are arbitrarily long extremal square-free ternary words. We find all lengths which admit an extremal square-free ternary word. In particular, we show that there is an extremal square-free ternary word of every sufficiently large length. We also solve the analogous problem for circular words.
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