A Ternary Square-free Sequence Avoiding Factors Equivalent to $abcacba$
Keywords: Words avoiding patterns, Square-free words
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 $n$.