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.

The picture shows me at my retirement conference at Queen Mary.

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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 24 October 2014

A problem

Given n and k with k < n, what is the smallest number d with the following property: given a set S of permutations of an n-set X generating a group G, and two k-subsets A and B of X in the same G-orbit, there is a product of at most d elements of S mapping A to B.

For k = 1, it is clear that n−1 suffices, and it is easy to construct examples showing this to be best possible.

I'm really interested in k = 2. Here n(n−1)/2−1 suffices, but I conjecture that the true value is much smaller (maybe a factor of 2 smaller?)

Old problems are kept here.