5-Abelian cubes are avoidable on binary alphabets

Abstract

<p> A k-abelian cube is a word uvw, where the factors u, v, and w are either pairwise equal, or have the same multiplicities for every one of their factors of length at most k. Previously it has been shown that k-abelian cubes are avoidable over a binary alphabet for k &gt;= 8. Here it is proved that this holds for k &gt;= 5.</p>