Mesosome Avoidance

Abstract

We consider avoiding mesosomes -- that is, words of the form $x{x}^{\prime }$ with $x^{\prime }$ 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.