We study extendability of ternary square-free words. Namely, we are interested in the square-free words that cannot be infinitely extended preserving square-freeness. We prove that any positive integer is the length of the longest extension of some ternary square-free word and thus solve an open problem by Allouche and Shallit. We also resolve the two-sided version of this problem. © 2012 Springer-Verlag.
CITATION STYLE
Petrova, E. A., & Shur, A. M. (2012). Constructing premaximal ternary square-free words of any level. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7464 LNCS, pp. 752–763). https://doi.org/10.1007/978-3-642-32589-2_65
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