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arXiv · 2408.00484

On set systems without singleton intersections

Danila Cherkashin
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Abstract

Consider a family $\mathcal{F}$ of $k$-subsets of an ambient $(k^2-k+1)$-set such that no pair of $k$-subsets in $\mathcal{F}$ intersects in exactly one element. In this short note we show that the maximal size of such $\mathcal{F}$ is $\binom{k^2-k-1}{k-2}$ for every $k > 1$.

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Danila Cherkashin. 2024-08-01. On set systems without singleton intersections. https://arxiv.org/abs/2408.00484

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