Repetition Avoidance in Curling-Number Transforms
Joint work on repetition avoidance in words and their curling-number transforms, combining morphic constructions, Walnut verification, and exhaustive finite searches.
This paper studies repetition avoidance simultaneously in an infinite or finite word and in its curling-number transform. For alphabets of sizes 2, 3, and 4, the work combines morphic constructions with exhaustive finite searches and automatic verification.
Among the main results, a ternary word for which both the word and its curling-number transform are overlap-free has length at most 84, while over a four-letter alphabet an infinite example exists. This shows that four is the smallest alphabet size allowing simultaneous infinite overlap-freeness.