Abstract
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.
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Petrova, E.A., Shur, A.M. (2012). Constructing Premaximal Ternary Square-Free Words of Any Level. In: Rovan, B., Sassone, V., Widmayer, P. (eds) Mathematical Foundations of Computer Science 2012. MFCS 2012. Lecture Notes in Computer Science, vol 7464. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32589-2_65
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DOI: https://doi.org/10.1007/978-3-642-32589-2_65
Publisher Name: Springer, Berlin, Heidelberg
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