2 research outputs found
A ternary square-free sequence avoiding factors equivalent to
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 . In fact, we: (1)
characterize all the (two-way) infinite ternary square-free words avoiding
letter pattern (2) characterize the lexicographically least (one-way)
infinite ternary square-free word avoiding letter pattern (3) show
that the number of ternary square-free words of length avoiding letter
pattern grows exponentially with .Comment: 7 pages, 1 figur
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.http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i2p4