Change of address 

The addresses of my webpages at St Andrews have changed: wwwcirca has changed to wwwgroups. Redirection means you shouldn't notice any changes, but you might want to update bookmarks or links. 
Welcome to my St Andrews homepage. This page is under construction (and probably always will be!)
I am a halftime 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.
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School of Mathematics and Statistics
University of St Andrews North Haugh St Andrews, Fife KY16 9SS SCOTLAND 
Tel.: +44 (0)1334 463769 Fax: +44 (0)1334 46 3748 Email: pjc20(at)starthurs(dot)ac(dot)uk [oops – wrong saint!] 
Page revised 18 May 2017 
A very specific problem. Let n = q^{2}+q+1, k = q+1. If it helps, suppose that a projective plane of order q exists. Let S be a collection of ksubsets of an nset 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 ≥ n_{0}(k) in 1983.
Old problems are kept here.