A Note on Square-Free Shuffles of Words

Abstract

We consider shuffles of words. It is first shown that there are infinite square-free words w over a four-letter alphabet such that w is a perfect shuffle of two square-free words u and v. Then we show that there exists an infinite square-free word u on three letters such that u can be shuffled with itself to produce another infinite square-free word. The proof of the latter result is constructive on finite factors, and it relies on a computer program for checking square-freeness of longer words.