向日葵:从土壤到油

Electron. Colloquium Comput. Complex. Pub Date : 2022-09-12 DOI:10.1090/bull/1777

Anup Rao

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引用次数: 3

摘要

向日葵是集合的集合，这些集合的成对相交是相同的。在这篇文章中，我们将去摘向日葵。我们在几个看似不相关的领域中发现了向日葵，然后讨论了Alweiss、Lovett、Wu和Zhang提出的著名的向日葵猜想Erdős和Rado的最新进展，以及Park和Pham发现的Kahn和Kalai的阈值与期望阈值猜想的相关解决方案。我们对这两个结果都给出了简短的证明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Sunflowers: from soil to oil

A sunflower is a collection of sets whose pairwise intersections are identical. In this article, we shall go sunflower-picking. We find sunflowers in several seemingly unrelated fields, before turning to discuss recent progress on the famous sunflower conjecture of Erdős and Rado, made by Alweiss, Lovett, Wu, and Zhang, as well as a related resolution of the threshold vs expectation threshold conjecture of Kahn and Kalai discovered by Park and Pham. We give short proofs for both of these results.

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Electron. Colloquium Comput. Complex.

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