Subsquares in random Latin rectangles
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918004896301056 |
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| author | Allsop, Jack Wanless, Ian M. |
| author_facet | Allsop, Jack Wanless, Ian M. |
| contents | Suppose that $k$ is a function of $n$ and $n\to\infty$. We show that with probability $1-O(1/n)$, a uniformly random $k\times n$ Latin rectangle contains no proper Latin subsquare of order $4$ or more, proving a conjecture of Divoux, Kelly, Kennedy and Sidhu. We also show that the expected number of subsquares of order 3 is bounded and find that the expected number of subsquares of order 2 is $\binom{k}{2}(1/2+o(1))$ for all $k\le n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08446 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subsquares in random Latin rectangles Allsop, Jack Wanless, Ian M. Combinatorics 05B15 Suppose that $k$ is a function of $n$ and $n\to\infty$. We show that with probability $1-O(1/n)$, a uniformly random $k\times n$ Latin rectangle contains no proper Latin subsquare of order $4$ or more, proving a conjecture of Divoux, Kelly, Kennedy and Sidhu. We also show that the expected number of subsquares of order 3 is bounded and find that the expected number of subsquares of order 2 is $\binom{k}{2}(1/2+o(1))$ for all $k\le n$. |
| title | Subsquares in random Latin rectangles |
| topic | Combinatorics 05B15 |
| url | https://arxiv.org/abs/2409.08446 |