Peter Cameron's homepage

Welcome to my St Andrews homepage. 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 My diary MathSciNet profile, Google Scholar Mathematical genealogy, Wikipedia page CV and publications (PDF) Short bio, some interviews On this site Teaching pages: MT5821, Advanced Combinatorics Independent study: Set theory and logic Talks, publications, conjectures, coauthors, students

Elsewhere My homepage at QMUL Papers on arXiv: mathematics, computer science, statistics Algebra and Combinatorics at St Andrews British Combinatorial Committee, BCC Conference List St Andrews seminars: Pure Maths, Algebra/Combinatorics Lecture notes Cameron Counts Walks page, Travel diaries Mathematical quotes The Infinite Quest, a short course from the IAI Academy Mathematics: the next generation (LMS–Gresham lecture)

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.