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 17 May 2016

A problem

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 n-cycle. 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 4-cycles 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.