Most frequent subsequences in a word
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908561697669120 |
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| author | Bukh, Boris Saatashvili, Aleksandre |
| author_facet | Bukh, Boris Saatashvili, Aleksandre |
| contents | We prove that every $n$-letter word over $k$-letter alphabet contains some word as a subsequence in at least $k^{n/4k(1+o(1))}$ many ways, and that this is sharp as $k\to\infty$. For fixed $k$, we show that the analogous number deviates from $μ_k^n$, for some constant $μ_k$, by a factor of at most $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22619 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Most frequent subsequences in a word Bukh, Boris Saatashvili, Aleksandre Combinatorics 68R15, 05D99 We prove that every $n$-letter word over $k$-letter alphabet contains some word as a subsequence in at least $k^{n/4k(1+o(1))}$ many ways, and that this is sharp as $k\to\infty$. For fixed $k$, we show that the analogous number deviates from $μ_k^n$, for some constant $μ_k$, by a factor of at most $n$. |
| title | Most frequent subsequences in a word |
| topic | Combinatorics 68R15, 05D99 |
| url | https://arxiv.org/abs/2509.22619 |