2023 Fiscal Year Final Research Report
Clusters of repetition roots
| Project/Area Number |
19K11815
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 60010:Theory of informatics-related
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| Research Institution | Akita University |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2024-03-31
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| Keywords | distinct repetitions / combinatorics / compressibility |
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| Outline of Final Research Achievements |
The research goal was to obtain better upper bounds on the number of distinct repetitions of the form xx...x that can occur in a sequence. We introduced a new approach to study the number of such repetitions through the set of positions their root x occurs in the sequence, called the cluster of the repetition. We aimed to show that each cluster must be larger than the number of other clusters included in it.
During the project we first proved that our conjecture about clusters in some special cases. In the final year we worked on extending a recent result by Brlek and Li that proved the upper bound on such repetitions equal to the length of the string divided by the exponent minus one, using Rauzy graphs. We managed to extend the approach to prove our conjecture regarding the clusters of distinct repetition roots. Our result opens up new directions for investigating repetitions in strings by considering the nested cluster structures of the repetition roots.
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| Free Research Field |
Computer science and combinatorics
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| Academic Significance and Societal Importance of the Research Achievements |
The significance of our results is that now we have better tools to study sequences containing many repetitions, which can lead to a better understanding of compression and pattern matching algorithms, which are of critical importance to our web infrastructure and computing in general.
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