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.

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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)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.