Repetition Avoidance in Circular Factors

Abstract

We consider the following novel variation on a classical avoidance problem from combinatorics on words: instead of avoiding repetitions in all factors of a word, we avoid repetitions in all factors where each individual factor is considered as a "circular word", i.e., the end of the word wraps around to the beginning. We determine the best possible avoidance exponent for alphabet size 2 and 3, and provide a lower bound for larger alphabets.