3-Abelian Cubes Are Avoidable on Binary Alphabets

摘要

A k-abelian cube is a word uvw, where u,v,w have the same factors of length at most k with the same multiplicities. Previously it has been known that k-abelian cubes are avoidable over a binary alphabet for k ≥ 5. Here it is proved that this holds for k ≥ 3.