Incompatible intersection properties

08/03/2018

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by   Peter Frankl, et al.

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Let F⊂ 2^[n] be a family in which any three sets have non-empty intersection and any two sets have at least 38 elements in common. The nearly best possible bound | F|< 2^n-2 is proved. We believe that 38 can be replaced by 3 and provide a simple-looking conjecture that would imply this.