A Ternary Square-free Sequence Avoiding Factors Equivalent to $abcacba$

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. .