Defect Effect of Bi-infinite Words in the Two-element Case

Abstract : 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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Discrete Mathematics and Theoretical Computer Science, DMTCS, 2001, 4 (2), pp.273-290
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Ján Maňuch. Defect Effect of Bi-infinite Words in the Two-element Case. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2001, 4 (2), pp.273-290. 〈hal-00958962〉

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