Extremal Infinite Overlap-Free Binary Words

Let t be the innite xed point, starting with 1, of the morphism :0 !01, 1! 10. An innite word overf0; 1g is said to be overlap-free if it contains no factor of the form axaxa, where a2f 0 ; 1gand x2f 0 ; 1g. We prove that the lexicographically least innite overlap-free binary word beginning with any specied prex, if it exists, has a sux which is a sux of t. In particular, the lexicographically least innite overlap-free binary word is 001001t.