Summary: Probabilistic Methods in Extremal Finite Set Theory
Department of Mathematics
Raymond and Beverly Sackler Faculty of Exact Sciences
Tel Aviv University, Tel Aviv, Israel
There are many known applications of the Probabilistic Method in Extremal Finite Set
Theory. In this paper we describe several examples, demonstrating some of the techniques used
and illustrating some of the typical results obtained. This is partly a survey paper, but it also
contains various new results.
Research supported in part by a United States Israel BSF Grant and by a Bergmann Memorial Grant
The Probabilistic Method is a powerful tool in tackling many problems in Combinatorics.
Roughly speaking, the method works as follows: Trying to prove that a combinatorial structure
(or a substructure of a given one) with certain desired properties exists, one defines an appropriate
probability space of structures and then shows that the desired properties hold in this space with
Extremal Finite Set Theory is one of the most rapidly developing areas in Combinatorics, which
has applications in various other branches of Mathematics and Computer Science including Discrete