The number of primitive words of unbounded exponent in the language of an HD0L-system is finite

Abstract

Let H be an HD0L-system. We show that there are only finitely many primitive words v with the property that $v^k$, for all integers k, is an element of the factorial language of H. In particular, this result applies to the set of all factors of a morphic word. We provide a formalized proof in the proof assistant Isabelle/HOL as part of the Combinatorics on Words Formalized project.