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.