The structure of the set of cube-free $ Z$-words in a two-letter alphabet
Arseny M. Shur · Izvestiya Mathematics · 2000
The object of our study is the set of -words, that is, (bi)infinite sequences of alphabetic symbols indexed by integers. We consider an ordered family of subsets of the set of all the cube-free -words in a two-letter alphabet. The construction of this family is based on the notion of the local exponent of a -word. The problem of existence of cube-free -words which are -words of local exponent 2 (the minimum possible) is described. An important distinction is drawn between strongly cube-free -words and -words of greater local exponent.