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.
On this site
School of Mathematics and Statistics
University of St Andrews
St Andrews, Fife KY16 9SS
Tel.: +44 (0)1334 463769
Fax: +44 (0)1334 46 3748
[oops – wrong saint!]
Page revised 6 March 2015
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.