I will be away from St Andrews from Tuesday 7 November to Saturday 2 December. Please contact me by email during that time. 
Welcome to my St Andrews homepage. This page is under construction (and probably always will be!)
I am a halftime 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 SCOTLAND 
Tel.: +44 (0)1334 463769 Fax: +44 (0)1334 46 3748 Email: pjc20(at)starthurs(dot)ac(dot)uk [oops – wrong saint!] 
Page revised 13 October 2017 
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 Gorbits on proper colourings of Γ with x colours.
We call the pair (Γ,G) a reciprocal pair if P_{Γ,G}(x) = (−1)^{n}GF_{G}(−x).
Problem: Find all reciprocal pairs.
See arXiv 1701.06954 for more information.
Old problems are kept here.