I am a Lecturer in Combinatorics in the Department of Computer and Information Sciences.
My research interests are in enumerative and extremal combinatorics, particularly in relation to permutations.
Recent research has resulted in the first general result concerning the exact growth rates of a broad family of permutation classes, published in the Transactions of the American Mathematical Society. Another paper, published in the Journal of the London Mathematical Society, uses a novel approach to yield an improved lower bound to the notorious problem of computing the growth rate of the class of permutations avoiding the pattern 1324.
“Enumeration, otherwise known as counting, is the oldest mathematical subject.”
— Doron Zeilberger, The Princeton Companion to Mathematics, 2008
“A generating function is a clothesline on which we hang up a sequence of numbers for display.”
— Herbert Wilf, generatingfunctionology, 1994
In the 1980s, following undergraduate studies in mathematics at the University of Oxford, I undertook some computer science research. For my Oxford M.Sc. dissertation, I developed a model for the denotational semantics of the concurrent programming language occam. Following this, I spent two years in industry with GEC, working on formalisms for specifying communications protocols, and, as part of a project to design a parallel machine to run functional programming languages, produced a paper that introduced weighted reference counting, now a key method for managing memory in distributed computer architectures.
This was followed by a career in software development, first as a developer, consultant and trainer for the Summer Institute of Linguistics, based in Papua New Guinea, and subsequently as a software engineer and development manager with Emtex Ltd. (acquired by Pitney Bowes in 2006).
A decade ago, I carried out some independent mathematical research in my spare time, resulting in the publication of a paper improving on a long-standing extremal result of Erdős and Füredi in discrete geometry.
In 2012, I left software development for full-time mathematical research, and in June 2015 was awarded a PhD in enumerative combinatorics from The Open University. My supervisor was Robert Brignall. The topic of my thesis is the growth of permutation classes. As a result of my doctoral studies, I produced five papers.
After completing my PhD, I was a Visiting Research Fellow at The Open University for a year, during which time I completed four more papers. Two of these concern the degree-diameter problem for Cayley graphs. The other two address specific enumerative questions in pattern-avoidance.