# On the maximum number of distinct intersections in an intersecting family

@article{Frankl2021OnTM, title={On the maximum number of distinct intersections in an intersecting family}, author={Peter Frankl and Sergei Kiselev and Andrey B. Kupavskii}, journal={Discret. Math.}, year={2021}, volume={345}, pages={112757} }

## 5 Citations

### An improved threshold for the number of distinct intersections of intersecting families

- Mathematics
- 2022

A family F of subsets of { 1 , 2 , . . . , n } is called a t -intersecting family if | F ∩ G | ≥ t for any two members F, G ∈ F and for some positive integer t . If t = 1, then we call the family F…

### Intersections and distinct intersections in cross-intersecting families

- MathematicsEuropean Journal of Combinatorics
- 2023

### Triangles in r-wise t-intersecting families

- Mathematics
- 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

- MathematicsMathematika
- 2022

We prove the following the generalized Turán type result. A collection T${\mathcal {T}}$ of r sets is an r‐triangle if for every T1,T2,⋯,Tr−1∈T$T_1,T_2,\dots ,T_{r-1}\in {\mathcal {T}}$ we have…

### Best possible bounds on the double-diversity of intersecting hypergraphs

- Mathematics
- 2022

For a family F ⊂ (cid:0) [ n ] k (cid:1) and two elements x, y ∈ [ n ] deﬁne F (¯ x, ¯ y ) = { F ∈ F : x / ∈ F, y / ∈ F } . The double-diversity γ 2 ( F ) is deﬁned as the minimum of |F (¯ x, ¯ y ) |…

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