Consider a family F of k-subsets of an ambient (k²-k+1) -set such that no pair of k-subsets in F intersects in exactly one element. In this short note we show that the maximal size of such F is k²-k-1k-2 for every k > 1.

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Danila Cherkashin (Thu,) studied this question.

synapsesocial.com/papers/68e5e1ceb6db643587575dd5 https://doi.org/https://doi.org/10.48550/arxiv.2408.00484

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1Set Systems Containing No Singleton Intersection and the Delsarte Number2026
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Set Systems Containing No Singleton Intersection and the Delsarte Number2026
2A semidefinite programming approach to cross $2$-intersecting families2025
3On a $d$-degree Erdős-Ko-Rado Theorem2024
4On set systems with strongly restricted intersections2024
5Intersecting families with large shadow degree2024