Dr David Bevan

Lecturer

Mathematics and Statistics

Personal statement

I am a Lecturer in Combinatorics. My research interests concern enumerative, asymptotic and extremal questions, particularly in relation to permutations.

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.

Current topics of research include enumerative and structural questions concerning grid classes of permutations, the enumeration and structure of the class of permutations avoiding the pattern 1324, and how the structure of a random permutation evolves as the number of its inversions increases.

✦✦✦ PhD Opportunities ✦✦✦

If you are interested in studying for a PhD in combinatorics and have your own source of funding, details of two projects can be found here and here, along with information on how to apply. Feel free to get in touch if you have any questions.

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 in the voluntary sector, based in Papua New Guinea, and subsequently as a software engineer and development manager in industry 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.

 

Publications

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 Vol 88 (2020)
https://doi.org/10.1016/j.ejc.2020.103115
Bijections between directed animals, multisets and Grand-Dyck paths
Baril Jean-Luc, Bevan David, Kirgizov Sergey
The Electronic Journal of Combinatorics Vol 27 (2020)
https://doi.org/10.37236/8826
Permutations with few inversions are locally uniform
Bevan David
Discrete Analysis (2019)
Intervals of permutation class growth rates
Bevan David
Combinatorica Vol 38, pp. 279-303 (2018)
https://doi.org/10.1007/s00493-016-3349-2
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)
https://doi.org/10.1016/j.jcta.2017.08.006
Large butterfly Cayley graphs and digraphs
Bevan David
Discrete Mathematics Vol 340, pp. 2432-2436 (2017)
https://doi.org/10.1016/j.disc.2017.05.012

More publications

Teaching

This year I'm teaching the following:

MM116 Mathematics 1c (Semester 1)

MM109 Applying Mathematics 2: Graph Theory

MM917 Networks in Finance

Past teaching responsibilities include 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 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); memory caching; virtual memory.

Research interests

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

Preprints

Recent publications

My older publications can be found on the following pages: ORCiD dblp Mendeley Scopus Google Scholar

Slides from talks

Mathematica demonstrations

 

dblp page

Professional activities

Graphs and Combinatorics (Journal)
Peer reviewer
8/2020
Algebraic Combinatorics (Journal)
Peer reviewer
3/2020
Contributions to Discrete Mathematics (Journal)
Peer reviewer
11/2019
Discrete Mathematics (Journal)
Peer reviewer
7/2019
Journal of Combinatorics (Journal)
Peer reviewer
1/2018
Discrete Applied Mathematics (Journal)
Peer reviewer
11/2017

More professional activities

Address

Mathematics and Statistics
Livingstone Tower

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