Avoidance of split overlaps

02/05/2020

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by   Daniel Gabric, et al.

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We generalize Axel Thue's familiar definition of overlaps in words, and show that there are no infinite words containing split occurrences of these generalized 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.