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A ternary square-free sequence avoiding factors equivalent to $abcacba$ (1603.03059v1)
Published 9 Mar 2016 in cs.FL
Abstract: 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: (1) characterize all the (two-way) infinite ternary square-free words avoiding letter pattern $xyzxzyx$ (2) characterize the lexicographically least (one-way) infinite ternary square-free word avoiding letter pattern $xyzxzyx$ (3) show that the number of ternary square-free words of length $n$ avoiding letter pattern $xyzxzyx$ grows exponentially with $n$.