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arXiv · 2606.30593

A Polynomial Improvement of Naslund--Sawin Bound for Sunflower-Free Families Using Triangular Tensors

Omran Ahmadi·Hassan Norouzi
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Abstract

Naslund and Sawin used the slice-rank method for diagonal tensors to prove that $$|\mathcal{F}|=O\!\left(n^{1/2}\left(\frac{3}{2^{2/3}}\right)^n\right)$$ for any sunflower-free family $\mathcal{F}\subseteq 2^{[n]}$. We prove a lemma similar to the slice-rank lemma for the newly defined $i$-triangular tensors, and use it to achieve a polynomial-factor improvement of the bound of Naslund and Sawin by proving that $$|\mathcal{F}|=O\!\left(n^{1/6}\left(\frac{3}{2^{2/3}}\right)^n\right)$$ for any sunflower-free family $\mathcal{F}\subseteq 2^{[n]}$.

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Omran Ahmadi, Hassan Norouzi. 2026-06-29. A Polynomial Improvement of Naslund--Sawin Bound for Sunflower-Free Families Using Triangular Tensors. https://arxiv.org/abs/2606.30593

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