• Corpus ID: 14770204

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
Intersecting families of sets and permutations: a survey
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
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
Set families with a forbidden pattern
• Mathematics, Computer Science
Eur. J. Comb.
• 2017

References

SHOWING 1-10 OF 27 REFERENCES
Families of finite sets with minimum shadows
• Mathematics, Computer Science
Comb.
• 1986
This paper deals with the extremal families, e.g., they are completely described for infinitely many values ofm, and is concerned with k-d-element subsets of these families.
INTERSECTION PROPERTIES OF SYSTEMS OF FINITE SETS
• Mathematics
• 1978
Let X be a finite set of cardinality n. IfL = {ll,...,l,}is a set of nonnegative integers with 11 enr-1(c = e(k) is a constant depending on k), then (i)there exists an
Intersection theorems with geometric consequences
• Mathematics, Computer Science
Comb.
• 1981
It is proved that ifℱ is a family ofk-subsets of ann-set, μ0, μ1, ..., μs are distinct residues modp (p is a prime) such thatk ≡ μ0 (modp) and forF ≠ F′ ≠ℽ there is one set within which all the distances are realised.
A generalization of a theorem of Kruskal
• M. Mörs
• Mathematics, Computer Science
Graphs Comb.
• 1985
This theorem generalizes a theorem which gives a solution for the problem without the condition and gives a necessary and sufficient condition for the uniqueness of the solution in the KKL theorem.
On Hypergraphs without Two Edges Intersecting in a Given Number of Vertices
• Computer Science, Mathematics
J. Comb. Theory, Ser. A
• 1984
Linear Dependencies among Subsets of a Finite Set
• Computer Science, Mathematics
Eur. J. Comb.
• 1983
It is proved that if (t + 1 1 ) , …, ( t + 1 k − t − 1 ) have a common divisor d which does not divide αi than ∃i' such that |Fi∩Fi'| = k −t − 1 (Theorem 1).
The realization of distances within sets in Euclidean space
• Mathematics
• 1972
In 1944 and 1945 H. Hadwiger [1, 2] proved the following theorems. Theorem A. Let E n be covered by n + 1 closed sets. Then there is one of the sets, within which all distances are realized. Theorem
Characterization off-vectors of families of convex sets inRd Part I: Necessity of Eckhoff’s conditions
LetK=K1,...,Kn be a family ofn convex sets inRd. For 0≦i<n denote byfi the number of subfamilies ofK of sizei+1 with non-empty intersection. The vectorf(K) is called thef-vectors ofK. In 1973 Eckhoff
INTERSECTION THEOREMS FOR SYSTEMS OF FINITE SETS
• Mathematics
• 1961
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
Problems and Results in Combinatorial Analysis
I gave many lectures by this and similar titles, many in fact in these conferences and I hope in my lecture in 1978 I will give a survey of the old problems and describe what happened to them. In the