A test-set fork-power-free binary morphisms

Abstract

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 k 2 . 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