We combine here Tao’s slice-rank bounding method and Gröbner basis techniques and apply it to the Erdős–Rado Sunflower Conjecture.
Let \({0\leq k\leq n}\) be integers. We prove that if \({\mathcal{F}}\) is a k-uniform family of subsets of [n] without a sunflower with 3 petals, then
This result allows us to improve slightly a recent upper bound of Naslund and Sawin for the size of a sunflower-free family in 2[n].
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Hegedűs, G. An improved upper bound for the size of a sunflower-free family. Acta Math. Hungar. 155, 431–438 (2018). https://doi.org/10.1007/s10474-018-0798-7
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DOI: https://doi.org/10.1007/s10474-018-0798-7