Old and new results on the union-closed sets conjecture
by
Koen Thas
Ghent University, Ghent, Belgium

A finite union-closed set (or family) V is a finite non-empty set of distinct finite sets which is closed under union. It is a longstanding conjecture - presumably first made by P. Frankl in 1979 - that if V is such a set, then there always is an element which is contained in at least half of the elements of V.
Especially in the last decade there has been a lot of work done on this conjecture in various fields of mathematics, such as in the theories of lattices, hypergraphs, animatroids, coding theory and even number theory.
In our talk, we will discuss old and new results on Frankl's conjecture.

Date received: April 17, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahh-08.