A Ternary Square-free Sequence Avoiding Factors Equivalent to abcacba
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Currie, James D.
James D. Currie. “A Ternary Square-free Sequence Avoiding Factors Equivalent to abcacba.” Electronic Journal of Combinatorics 23(2) (2016) P2.41,http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i2p41
We solve a problem of Petrova, finalizing the classification of letter patterns avoidable by ternary square-free words; we show that there is a ternary square-free word avoiding letter pattern xyzxzyx. In fact, we characterize all the (two-way) infinite ternary square-free words avoiding letter pattern xyzxzyx characterize the lexicographically least (one-way) infinite ternary square-free word avoiding letter pattern xyzxzyx show that the number of ternary square-free words of length n avoiding letter pattern xyzxzyx grows exponentially with n.