随机拉丁方格中的子方格

arXiv - MATH - Combinatorics Pub Date : 2024-09-13 DOI:arxiv-2409.08446

Jack Allsop, Ian M. Wanless

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引用次数: 0

摘要

我们证明，随着 $n \to \infty$ 的概率为 1-o(1)$ ，阶为 $n$ 的均匀随机拉丁方阵不包含阶为 $4$ 或更多的子方阵，从而解决了麦凯和万利斯的猜想。我们还证明了阶为 3 的子方格的预期数目是有界的。

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Subsquares in random Latin squares

We prove that with probability $1-o(1)$ as $n \to \infty$, a uniformly random Latin square of order $n$ contains no subsquare of order $4$ or more, resolving a conjecture of McKay and Wanless. We also show that the expected number of subsquares of order 3 is bounded.

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arXiv - MATH - Combinatorics

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