# Intersection Theorems for Finite Sets and Geometric Applications

@inproceedings{Frankl2010IntersectionTF, title={Intersection Theorems for Finite Sets and Geometric Applications}, author={Peter Frankl}, year={2010} }

1. Introduction. Let X be an n-element set and F C 2 X a family of distinct subsets of X. Suppose that the members of F satisfy some conditions. What is the maximum (or minimum) value of |F|—this is the generic problem in extremal set theory. There have been far too many papers and results in this area to be overviewed in such a short paper. Therefore, we will only deal with some intersection theorems. The simplest is

## 6 Citations

Intersecting families of sets and permutations: a survey

- Mathematics
- 2011

A family A of sets is said to be t-intersecting if any two sets in A have at least t common elements. A central problem in extremal set theory is to determine the size or structure of a largest…

The maximum sum and the maximum product of sizes of cross-intersecting families

- Computer Science, MathematicsEur. J. Comb.
- 2014

An Erdos-Ko-Rado theorem for the derangement graph of PGL(2, q) acting on the projective line

- Computer Science, MathematicsJ. Comb. Theory, Ser. A
- 2011

Intersecting families of extended balls in the Hamming spaces

- Mathematics
- 2014

A family $\mathcal{F}$ of subsets of a set $X$ is $t$-intersecting if $\vert A_i \cap A_j \vert \geq t$ for every $A_i, \; A_j \in \mathcal{F}$. We study intersecting families in the Hamming…

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