Disposability in Square-Free Words

preprint2020arXivOpen access

Abstract

We consider words ww over the alphabet Σ={0,1,2}Σ=\{0,1,2\}. It is shown that there are irreducibly square-free words of all lengths nn except 4,5,7 and 12. Such a word is square-free (i.e., it has no repetitions uuuu as factors), but by removing any one internal letter creates a square in the word.

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