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. In addition, I am an associate researcher at CEMAT, University of Lisbon, and a teacher at Universidade Aberta, Portugal.

I am a Fellow of the Royal Society of Edinburgh.

About me

On this site

Me

Elsewhere


Research snapshots

Integrable groups

With João Araujo and Francesco Matucci, I determined the set of natural numbers n with the property that every group of order n is the derived subgroup of some group. This set is closely related to (but slightly larger than) the set of n for which every group of order n is abelian. We also showed that if a finite group is a derived group, then it is the derived group of a finite group.

Equitable partitions of Latin square graphs

With Rosemary Bailey, Alexander Gavrilyuk, and Sergey Goryainov, I determined the equitable partitions of Latin square graphs under an extra assumption on eigenvalues. A partition is equitable if, given any two parts, the number of neighbours in the second part of a vertex in the first depends only on the parts and not on the chosen vertex.

Power graphs of torsion-free groups

In the directed power graph of a group, there is an arc from x to y if y is a power of x; for the undirected power graph, just ignore directions. The power graph does not in general determine the directed power graph, even up to isomorphism (though it does for finite groups). With Horacio Guerra and Šimon Jurina, I showed that for various torsion-free groups, the directions are indeed determined.


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 1 February 2018

A problem

The cycle polynomial FG(x) of a permutation group G is the polynomial ∑{xc(g) : gG}, where c(g) is the number of cycles of g (including fixed points).

The orbital chromatic polynomial PΓ,G(x) of the graph Γ and subgroup G of Aut(Γ) is the polynomial whose value at the positive integer x is the number of G-orbits on proper colourings of Γ with x colours.

We call the pair (Γ,G) a reciprocal pair if PΓ,G(x) = (−1)n|G|FG(−x).

Problem: Find all reciprocal pairs.

See arXiv 1701.06954 for more information.

Old problems are kept here.