Avoidance of split overlaps
2021
Abstract We generalize Axel Thue’s familiar definition of overlaps in words, and observe that there are no infinite words avoiding split occurrences of these generalized overlaps. We give estimates for the length of the longest finite word that avoids split overlaps. Along the way we prove a useful theorem about repeated disjoint occurrences in words — an interesting natural variation on the classical de Bruijn sequences.
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