Recovery of cyclic words by their subwords
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915649619492864 |
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| author | Luchinin, Sergey Puzynina, Svetlana Rao, Michaël |
| author_facet | Luchinin, Sergey Puzynina, Svetlana Rao, Michaël |
| contents | A problem of reconstructing words from their subwords involves determining the minimum amount of information needed, such as multisets of scattered subwords of a specific length or the frequency of scattered subwords from a given set, in order to uniquely identify a word. In this paper we show that a cyclic word on a binary alphabet can be reconstructed by its scattered subwords of length $\frac34n+4$, and for each $n$ one can find two cyclic words of length $n$ which have the same set of scattered subwords of length $\frac34n-\frac32$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03289 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Recovery of cyclic words by their subwords Luchinin, Sergey Puzynina, Svetlana Rao, Michaël Discrete Mathematics Combinatorics 68R15 A problem of reconstructing words from their subwords involves determining the minimum amount of information needed, such as multisets of scattered subwords of a specific length or the frequency of scattered subwords from a given set, in order to uniquely identify a word. In this paper we show that a cyclic word on a binary alphabet can be reconstructed by its scattered subwords of length $\frac34n+4$, and for each $n$ one can find two cyclic words of length $n$ which have the same set of scattered subwords of length $\frac34n-\frac32$. |
| title | Recovery of cyclic words by their subwords |
| topic | Discrete Mathematics Combinatorics 68R15 |
| url | https://arxiv.org/abs/2412.03289 |