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}
}

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

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

Triangles in r-wise t-intersecting families

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

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

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 ) |

References

SHOWING 1-8 OF 8 REFERENCES

On intersecting families of finite sets

  • P. Frankl
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 1980
Whenever F is an extremal family the authors can find a 7-3 Steiner system B such that F consists exactly of those k -subsets of X which contain some member of B .

Intersection Theorems for Systems of Sets

A version of Dirichlet's box argument asserts that given a positive integer a and any a2 +1 objects x0 , x1 , . . ., xa 2, there are always a+1 distinct indices v (0 < v < a 2) such that the

Problems and Results on 3-chromatic Hypergraphs and Some Related Questions

A hypergraphi is a collection of sets. This paper deals with finite hy-pergraphs only. The sets in the hypergraph are called edges, the elements of these edges are points. The degree of a point is

INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS

2. Notation The letters a, b, c, d, x, y, z denote finite sets of non-negative integers, all other lower-case letters denote non-negative integers. If fc I, then [k, I) denotes the set