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 |
| _version_ | 1797270226002247680 |
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| author | Ján Maňuch |
| author_facet | Ján Maňuch |
| author_sort | Ján Maňuch |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-25T02:00:54Z |
| format | Article |
| id | doaj.art-a922d248fe92468fb15aefe15b41f5a6 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:54Z |
| publishDate | 2001-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-a922d248fe92468fb15aefe15b41f5a62024-03-07T15:04:11ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502001-01-01Vol. 4 no. 210.46298/dmtcs.279279Defect Effect of Bi-infinite Words in the Two-element CaseJán Maňuch0Department of MathematicsLet 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.https://dmtcs.episciences.org/279/pdfdefect effectbi-infinite words[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Ján Maňuch Defect Effect of Bi-infinite Words in the Two-element Case Discrete Mathematics & Theoretical Computer Science defect effect bi-infinite words [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Defect Effect of Bi-infinite Words in the Two-element Case |
| title_full | Defect Effect of Bi-infinite Words in the Two-element Case |
| title_fullStr | Defect Effect of Bi-infinite Words in the Two-element Case |
| title_full_unstemmed | Defect Effect of Bi-infinite Words in the Two-element Case |
| title_short | Defect Effect of Bi-infinite Words in the Two-element Case |
| title_sort | defect effect of bi infinite words in the two element case |
| topic | defect effect bi-infinite words [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/279/pdf |
| work_keys_str_mv | AT janmanuch defecteffectofbiinfinitewordsinthetwoelementcase |