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
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 6 March 2015

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.