Mesosome avoidance

We consider avoiding mesosomes—that is, words of the form x x ′ with x ′ a conjugate of x that is different from x —over a binary alphabet. We give a structure theorem for mesosome-avoiding words, count how many there are, characterize all the infinite mesosome-avoiding words, and determine the minimal forbidden words. • Investigates a new type of repetition in words, the mesosome. • Characterizes both finite and infinite mesosome-avoiding binary words. • Counts the number of length- n mesosome-avoiding binary words.