A test-set fork-power-free binary morphisms
Francis Wlazinski · RAIRO - Theoretical Informatics and Applications · 2001
A morphism f is k-power-free if and only if f(w) is k-power-free whenever w is a k-power-free word. A morphism f is k-power-free up to m if and only if f(w) is k-power-free whenever w is a k-power-free word of length at most m. Given an integer k ≥ 2, we prove that a binary morphism is k-power-free if and only if it is k-power-free up to k2. This bound becomes linear for primitive morphisms: a binary primitive morphism is k-power-free if and only if it is k-power-free up to 2k+1