Square-free shuffles of words

Let u v denote the set of all shuffles of the words u and v . It is shown that for each integer n ≥ 3 there exists a square-free ternary word u of length n such that u u contains a square-free word. This property is then shown to also hold for infinite words, i.e., there exists an infinite square-free word u on three letters such that u can be shuffled with itself to produce an infinite square-free wordw ∈ u u .