The repetition threshold for binary rich words
A word of length $n$ is rich if it contains $n$ nonempty palindromic factors. An infinite word is rich if all of its finite factors are rich. Baranwal and Shallit produced an infinite binary rich word with critical exponent $2+\sqrt{2}/2$ ($\approx 2.707$) and conjectured that this was the least pos...
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| Published in: | Discrete Mathematics and Theoretical Computer Science Vol. 22 no. 1; no. Analysis of Algorithms; pp. 1 - 16 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Nancy
DMTCS
01.01.2020
Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| ISSN: | 1365-8050, 1462-7264, 1365-8050 |
| Online Access: | Get full text |
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| Summary: | A word of length $n$ is rich if it contains $n$ nonempty palindromic factors. An infinite word is rich if all of its finite factors are rich. Baranwal and Shallit produced an infinite binary rich word with critical exponent $2+\sqrt{2}/2$ ($\approx 2.707$) and conjectured that this was the least possible critical exponent for infinite binary rich words (i.e., that the repetition threshold for binary rich words is $2+\sqrt{2}/2$). In this article, we give a structure theorem for infinite binary rich words that avoid $14/5$-powers (i.e., repetitions with exponent at least 2.8). As a consequence, we deduce that the repetition threshold for binary rich words is $2+\sqrt{2}/2$, as conjectured by Baranwal and Shallit. This resolves an open problem of Vesti for the binary alphabet; the problem remains open for larger alphabets.
Comment: 16 pages |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1365-8050 1462-7264 1365-8050 |
| DOI: | 10.23638/DMTCS-22-1-6 |