Unbordered factors and Lyndon words Original Research Article

A primitive word image is a Lyndon word if image is minimal among all its conjugates with respect to some lexicographic order. A word image is bordered if there is a nonempty word u such that image for some word image. A right extension of a word image of length n is a word wu where all factors longer than n are bordered. A right extension wu of image is called trivial if there exists a positive integer k such that image for some word image. We prove that Lyndon words have only trivial right extensions. Moreover, we give a conjecture which characterizes a property of every word image which has a nontrivial right extension of length image.