Peter Cameron's homepage

Welcome to my St Andrews homepage. Under construction This page is under construction (and probably always will be!)

I am a half-time Professor in the School of Mathematics and Statistics at the University of St Andrews, and an Emeritus Professor of Mathematics at Queen Mary, University of London.

About me

On this site



School of Mathematics and Statistics
University of St Andrews
North Haugh
St Andrews, Fife KY16 9SS
Tel.: +44 (0)1334 463769
Fax: +44 (0)1334 46 3748
Email: pjc20(at)st-arthurs(dot)ac(dot)uk
  [oops – wrong saint!]

Page revised 18 May 2017

A problem

A very specific problem. Let n = q2+q+1, k = q+1. If it helps, suppose that a projective plane of order q exists. Let S be a collection of k-subsets of an n-set X, with the property that the intersection of two members of S does not have cardinality 1. The size of such a set is at most {n choose k}/n. Suppose that S attains this bound.

Problem: Is it true that, if q > 2, then the cardinality of the intersection of two members of S must be at least 2?

Note that Frankl and Füredi proved an analogous result under the assumption n ≥ n0(k) in 1983.

Old problems are kept here.