Defect Effect of Bi-infinite Words in the Two-element Case
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 \emphK...
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Format: | Article |
Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2001-01-01
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Series: | Discrete Mathematics & Theoretical Computer Science |
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Online Access: | https://dmtcs.episciences.org/279/pdf |
Summary: | 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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ISSN: | 1365-8050 |