Critical factorisation in square-free words

A position p in a word w is critical if the minimal local period at equal to global of . According Critical Factorisation Theorem all words length least two have point. We study number η ( ) points square-free ternary , i.e. over three letter alphabet. show that sufficiently long satisfy ≤| |− 5 where | denotes Moreover, bound reached by infinitely many words. On other hand, every has |∕4 points, and there sequence these closing this bound.