School of Mathematical Sciences

Unions and intersections of finite sets menu

Unions and intersections of finite sets

Anthony Hilton (QMUL)
Fri, 03/03/2017 - 16:00
Queen's building W316
Seminar series: 

In the early 70's Daykin conjectured that a family of subsets of
{1,2,...,n} which has the intersection property (i.e. any two subsets have
a non-empty intersection) and the non-union property (i.e the union of any
two subsets is not equal to {1,2,...,n}) contains at most 2^(n-2) members.
Different solutions of this conjecture were found within the next two of
three years by Schonheim, Seymour, (Daykin and Lovasz), and Hilton.
I will discuss various applications of the proofs and some
generalizations of the result.