Geodesic
The structure of the set of cube-free $Z$-words in a~two-letter alphabet
Izvestiya. Mathematics , Tome 64 (2000) no. 4, pp. 847-871

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The object of our study is the set of $Z$-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 $Z$-words in a two-letter alphabet. The construction of this family is based on the notion of the local exponent of a $Z$-word. The problem of existence of cube-free $Z$-words which are $Z$-words of local exponent 2 (the minimum possible) is described. An important distinction is drawn between strongly cube-free $Z$-words and $Z$-words of greater local exponent. 
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     title = {The structure of the set of cube-free $Z$-words in a~two-letter alphabet},
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A. M. Shur. The structure of the set of cube-free $Z$-words in a~two-letter alphabet. Izvestiya. Mathematics , Tome 64 (2000) no. 4, pp. 847-871. http://geodesic.mathdoc.fr/item/IM2_2000_64_4_a7/