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.

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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 22 October 2017

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.