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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2512.12077 |
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| _version_ | 1866918247963557888 |
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| author | He, Xiaoyu Post, Logan |
| author_facet | He, Xiaoyu Post, Logan |
| contents | A binary shuffle square is a binary word of even length that can be partitioned into two disjoint, identical subwords. Huang, Nam, Thaper, and the first author conjectured that as $n\rightarrow \infty$, asymptotically half of all binary words of length $2n$ are shuffle squares. We prove this conjecture in a strong form, by showing that the number of binary shuffle squares of length $2n$ is $(\frac{1}{2} - o(n^{-1/15})) 2^{2n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12077 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotically half of binary words are shuffle squares He, Xiaoyu Post, Logan Combinatorics 05A05 A binary shuffle square is a binary word of even length that can be partitioned into two disjoint, identical subwords. Huang, Nam, Thaper, and the first author conjectured that as $n\rightarrow \infty$, asymptotically half of all binary words of length $2n$ are shuffle squares. We prove this conjecture in a strong form, by showing that the number of binary shuffle squares of length $2n$ is $(\frac{1}{2} - o(n^{-1/15})) 2^{2n}$. |
| title | Asymptotically half of binary words are shuffle squares |
| topic | Combinatorics 05A05 |
| url | https://arxiv.org/abs/2512.12077 |