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arXiv · 2212.07821

Stability through non-shadows

Jun Gao·Hong Liu·Zixiang Xu
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Abstract

We study families $\mathcal{F}\subseteq 2^{[n]}$ with restricted intersections and prove a conjecture of Snevily in a stronger form for large $n$. We also obtain stability results for Kleitman's isodiametric inequality and families with bounded set-wise differences. Our proofs introduce a new twist to the classical linear algebra method, harnessing the non-shadows of $\mathcal{F}$, which may be of independent interest.

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Jun Gao, Hong Liu, Zixiang Xu. 2023-06-25. Stability through non-shadows. https://arxiv.org/abs/2212.07821

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