Extending Dekking's construction of an infinite binary word avoiding abelian $4$-powers

Abstract

We construct an infinite binary word with critical exponent 3 that avoids abelian 4-powers. Our method gives an algorithm to determine if certain types of morphic sequences avoid additive powers. We also show that there are Ω(1.172 n ) binary words of length n that avoid abelian 4-powers, which improves on previous estimates.