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Note on Sunflowers

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arxiv 2009.09327 v2 pith:XESBDTEZ submitted 2020-09-20 math.CO cs.DM

Tolson Bell , Suchakree Chueluecha , Lutz Warnke This is my paper · ORCID
classification math.COcs.DM
keywords sunflowernotepetalssetssufficesalweissboundbreakthrough
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A sunflower with p petals consists of p sets whose pairwise intersections are identical. The goal of the sunflower problem is to find the smallest r=r(p,k) such that any family of r^k distinct k-element sets contains a sunflower with p petals. Building upon a breakthrough of Alweiss, Lovett, Wu and Zhang from 2019, Rao proved that r=O(p log(pk)) suffices; this bound was reproved by Tao in 2020. In this short note we record that r=O(p log k) suffices, by using a minor variant of the probabilistic part of these recent proofs.

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  1. Maximal sets of a given diameter in Hamming cubes

    math.CO 2025-07 conditional novelty 7.0 of 10

    A d-maximal subset of the n-letter Hamming cube that contains no unit ball has size at most roughly n^d, and related bounds show all finite d-maximal sets are bounded and finitely many up to isomorphism.

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