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 25 April 2016 
Given a tree T on vertex set {1,…,n}, the edges form a set of n−1 transpositions whose product (in any order) is an ncycle. If T is a star, then the (n−1)! orderings of the edges give rise to the (n−1)! cycles, each exactly once; but for any other shape of tree, we do not have a bijection. e.g. for the path on 4 vertices, of the six 4cycles we obtain two twice, two once, and two not at all.
Problem: What is the distribution of frequencies of occurrence of cycles arising from orders of a given tree T?
Old problems are kept here.