# Best possible bounds on the number of distinct differences in intersecting families

@article{Frankl2021BestPB, title={Best possible bounds on the number of distinct differences in intersecting families}, author={Peter Frankl and S. G. Kiselev and Andrey B. Kupavskii}, journal={ArXiv}, year={2021}, volume={abs/2106.05355} }

For a family F , let D(F) stand for the family of all sets that can be expressed as F ∖ G, where F,G ∈ F . A family F is intersecting if any two sets from the family have non-empty intersection. In this paper, we study the following question: what is the maximum of |D(F)| for an intersecting family of k-element sets? Frankl conjectured that the maximum is attained when F is the family of all sets containing a fixed element. We show that this holds if n > 50k log k and k > 50. At the same time…

## 3 Citations

On the maximum number of distinct intersections in an intersecting family

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Triangles in r-wise t-intersecting families

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- 2022

Let t , r , k and n be positive integers and F a family of k -subsets of an n -set V . The family F is r -wise t -intersecting if for any F 1 , . . . , F r ∈ F , we have |∩ ri =1 F i | > t . An r…

Triangles in intersecting families

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We prove the following the generalized Turán type result. A collection T of r sets is an r-triangle if for every T1, T2, . . . , Tr−1 ∈ T we have ∩ r−1 i=1 Ti 6= ∅, but ∩T∈T T is empty. A family F of…

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