Dr David Bevan


Computer and Information Sciences

Personal statement

I am a Lecturer in Combinatorics in the Department of Computer and Information Sciences.

My research interests are in enumerative, asymptotic and extremal combinatorics, particularly in relation to permutation classes.

Enumerative combinatorics is concerned with counting, either exactly or approximately, the number of discrete structures satisfying certain constraints. Asymptotic combinatorics is to do with determining the structure and properties of typical large discrete objects. Extremal combinatorics concerns determining the size of the largest possible discrete structures of a given type.

A bit of background

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, during which I 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, based in Papua New Guinea, and subsequently as a software engineer and development manager in the UK.

In my spare time, I carried out some independent mathematical research 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 2015 was awarded a PhD from The Open University. The topic of my thesis was the growth of permutation classes. Following a year as a Visiting Research Fellow and Associate Lecturer at The Open University, I took up my current position in September 2016.



A structural characterisation of Av(1324) and new bounds on its growth rate
Bevan David, Brignall Robert, Elvey Price Andrew, Pantone Jay
European Journal of Combinatorics (2019)
Intervals of permutation class growth rates
Bevan David
Combinatorica Vol 38, pp. 279-303 (2018)
Prolific permutations and permuted packings : downsets containing many large patterns
Bevan David, Homberger Cheyne, Tenner Bridget Eileen
Journal of Combinatorial Theory Series A Vol 153, pp. 98-121 (2018)
Large butterfly Cayley graphs and digraphs
Bevan David
Discrete Mathematics Vol 340, pp. 2432-2436 (2017)
Staircases, dominoes, and the growth rate of 1324-avoiders
Bevan David, Brignall Robert, Elvey Price Andrew, Pantone Jay
European Conference on Combinatorics, Graph Theory and Applications, pp. 123–129 (2017)
The permutation class Av(4213,2143)
Bevan David
Discrete Mathematics and Theoretical Computer Science Vol 18 (2017)

more publications


My current teaching includes the following:

CS103 Machines, Languages and Computation (Semester 2)

Propositional logic and proofs using natural deduction; normal forms and satisfiability; computational complexity, P and NP; finite state automata and regular expressions, the Brzozowski algebraic method and the pumping lemma; Turing machines, undecidability, the halting problem and the Entscheidungsproblem.

CS104 Information and Information Systems (Module 1: Information Theory)

Data and information (syntax and semantics, text encodings, Unicode and UTF-8); error detection and correction (repetition codes, parity bits and Hamming codes); data compression (run-length encoding, Huffman coding and LZW); measuring information (entropy) and Shannon's Source Coding Theorem.

CS106 Computer Systems and Organisation (Semester 2)
CS107 Fundamentals of Computer Systems

Computer organization; MIPS assembly programming and the MIPS Instruction Set Architecture (registers, memory addressing, logical and shifting operations, jumps and branches, loops and arrays, integers and integer arithmetic, subroutines and the call stack, recursion); exceptions; memory caching; virtual memory.

Research interests

My research interests concern aspects of enumerative, asymptotic and extremal combinatorics, particularly with relation to permutations.


Recent publications

My Google Scholar page and my dblp page include older publications.

Slides from talks

Mathematica demonstrations

Professional activities

Discrete Mathematics (Journal)
Peer reviewer
Journal of Combinatorics (Journal)
Peer reviewer
Discrete Applied Mathematics (Journal)
Peer reviewer
Journal of Integer Sequences (Journal)
Peer reviewer
Prolific permutations and permuted packings
Combinatorica (Journal)
Peer reviewer

more professional activities


Computer and Information Sciences
Livingstone Tower

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