Geodesic
Defect Effect of Bi-infinite Words in the Two-element Case
Discrete mathematics & theoretical computer science, Tome 4 (2000-2001) no. 2.

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Let X be a two-element set of words over a finite alphabet. If a bi-infinite word possesses two X-factorizations which are not shiftequivalent, then the primitive roots of the words in X are conjugates. Note, that this is a strict sharpening of a defect theorem for bi-infinite words stated in \emphKMP. Moreover, we prove that there is at most one bi-infinite word possessing two different X-factorizations and give a necessary and sufficient conditions on X for the existence of such a word. Finally, we prove that the family of sets X for which such a word exists is parameterizable. 
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     author = {Ma\v{n}uch, J\'an},
     title = {Defect {Effect} of {Bi-infinite} {Words} in the {Two-element} {Case}},
     journal = {Discrete mathematics & theoretical computer science},
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Maňuch, Ján. Defect Effect of Bi-infinite Words in the Two-element Case. Discrete mathematics & theoretical computer science, Tome 4 (2000-2001) no. 2. doi : 10.46298/dmtcs.279. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.279/

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