Constructing Premaximal Ternary Square-Free Words of Any Level
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.
KeywordsFactor Order Simple Cycle Acyclic Digraph Word Versus Closed Walk
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