Peter Cameron's homepage

Welcome to my new homepage on GitHub. Under construction This page is under construction (and probably always will be!)

I am a quarter-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. In addition, I am an associate researcher at CEMAT, University of Lisbon, Portugal.

I am a Fellow of the Royal Society of Edinburgh.

About me

On this site



Research snapshots


A base for a permutation group is a sequence (a1,…,ar) of points in the permutation domain whose pointwise stabiliser is the identity. A base is irredundant if no point in the base is fixed by the stabiliser of its predecessors; it is minimal if no point in the base is fixed by the stabiliser of all the others.

A couple of things are clear:

In 1995, Dima Fon-Der-Flaass and I showed that the three conditions on irredundant bases, namely

are all equivalent. We call groups having this property IBIS groups.

Recently several people (Murray Whyte, Scott Harper, Pablo Spiga, maybe others) asked whether the set of sizes of irredundant bases form an interval. This is true. However, the analogue for minimal bases is false. For any integer d > 1, there is a group whose minimal bases have sizes 1 and d only. However, it is not yet known whether they do form an interval if the permutation group is required to be transitive.

A further question is: What happens for greedy bases? One of these is found by choosing the next base point in an orbit of maximum size for the stabiliser of its predecessors. (There is some variability because there might be a number of orbits of the same size.)

Old research snapshots are kept here.

I am Honorary Editor-In-Chief of the Australasian Journal of Combinatorics, an international open-access journal published by the Combinatorial Mathematics Society of Australasia. SCImago Journal & Country Rank

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 13 April 2023

A problem

A (total) ordering of a finite vector space is called compatible if every order-preserving bijection between subspaces of the same dimension is linear.

It is straightforward to show that every finite vector space has a compatible ordering: for example, choose any ordering of the finite field F; then the lexicographic ordering of Fn is compatible, for any n.

Problem: How many compatible orderings does the n-dimensional vector space over the field of order q have? (Formulae are known for the cases n = 1 and n = 2.)

Old problems are kept here.