Palindrome positions in ternary square-free words

Abstract

We answer a question of Brešar et al. about the structure of non-repetitive words: For any sequence A of positive integers with large enough gaps, there is a ternary non-repetitive word having a length 3 palindrome starting at each position a ∈ A . In fact, we can find ternary non-repetitive words such that for each a ∈ A , the length 3 subword starting at position a is a palindrome or not, as one chooses. This arbitrariness in the positioning of subwords contrasts markedly with the situation for binary overlap-free words.