Peter Cameron's homepage

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.

About me My diary MathSciNet profile, Google Scholar Mathematical genealogy, Wikipedia page CV and publications (PDF) Short bio, some interviews On this site Teaching pages: MT5821, Advanced Combinatorics Independent study: Set theory and logic Talks, publications, conjectures, coauthors, students

Elsewhere My homepage at QMUL Papers on arXiv: mathematics, computer science, statistics Algebra and Combinatorics at St Andrews British Combinatorial Committee, BCC Conference List St Andrews seminars: Pure Maths, Algebra/Combinatorics Lecture notes Cameron Counts Walks page, Travel diaries Mathematical quotes The Infinite Quest, a short course from the IAI Academy Mathematics: the next generation (LMS–Gresham lecture)

A problem

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

The orbital chromatic polynomial P_Γ,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 P_Γ,G(x) = (−1)ⁿ|G|F_G(−x).

Problem: Find all reciprocal pairs.

See arXiv 1701.06954 for more information.

Old problems are kept here.