Avoiding letter patterns in ternary square-free words

Abstract

We consider special patterns of lengths 5 and 6 in a ternary alphabet. We show that some of them are unavoidable in square-free words and prove avoidability of the other ones. Proving the main results, we use Fibonacci words as codes of ternary words in some natural coding system and show that they can be decoded to square- free words avoiding the required patterns. Furthermore, we estimate the minimal local (critical) exponents of square-free words with such avoidance properties. © 2016, Australian National University. All rights reserved.