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.

中文翻译：

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无阴影的稳定性

我们研究具有受限交集的族\({\mathcal {F}}\subseteq 2^{[n]}\)并以更强的形式证明大n的 Snevily 猜想。我们还获得了克莱特曼等径不等式和具有有界集合差异的族的稳定性结果。我们的证明为经典线性代数方法引入了一个新的转折，利用了\({\mathcal {F}}\)的非阴影，这可能是独立的兴趣。