Abstract:
Given a finite alphabet A, and an endomorphism h on A, we can call h 'almost primitivity-preserving' if, with up to finitely many exceptions, it takes primitive words into primitive words. If h is not almost primitivity preserving, call it a primitivity destroyer. If h is injective, we can look at the number of letters in A, n = |A| and ask: what is the smallest n for which we can construct a morphism that destroys primitivity? In particular, we'll see that the problem is closely connected to the study of repeated regions in a finite word (periodicity).