# 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}
}
• Published 1 August 2021
• Mathematics
• Discret. Math.
• 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
• 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
• Mathematics
Mathematika
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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
• 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 ) |