• United Kingdom

Accepting PhD Students

PhD projects

The Evolution of the Random Permutation Monotone Grid Classes of Permutations

20062020

Research output per year

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Personal profile

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 ✦✦✦

A fully funded PhD studentship is now available to investigate The Evolution of the Random Permutation. This concerns a permutation analogue of the celebrated Erdős–Rényi model of the random graph. More details, and information on how to apply can be found here. The deadline for applications is 12 June 2020.

If you have your own funding, details of another project can be found here. Feel free to get in touch if you have 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.

 

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

Teaching Interests

Recent 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.

Education/Academic qualification

Doctor of Philosophy, Open University

20122015

Bachelor of Arts, London Bible College

19861989

Master of Science, University of Oxford

19831984

Master of Arts, University of Oxford

19801983

External positions

Visiting Research Fellow, Open University

Aug 2015Oct 2016

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Research Output

  • 14 Article
  • 1 Conference Contribution
  • 1 Doctoral Thesis

Bijections between directed animals, multisets and Grand-Dyck paths

Baril, J-L., Bevan, D. & Kirgizov, S., 17 Apr 2020, In : The Electronic Journal of Combinatorics. 27, 2, 12 p., P2.10.

Research output: Contribution to journalArticle

Open Access
File
  • 2 Downloads (Pure)

    A structural characterisation of Av(1324) and new bounds on its growth rate

    Bevan, D., Brignall, R., Elvey Price, A. & Pantone, J., 17 Apr 2019, (Accepted/In press) In : European Journal of Combinatorics.

    Research output: Contribution to journalArticle

    Open Access
    File
  • 2 Downloads (Pure)

    Activities

    • 12 Journal peer review
    • 2 Organiser of major conference
    • 1 Organiser of special symposia
    • 1 Invited talk

    Discrete Mathematics (Journal)

    David Bevan (Peer reviewer)
    Jul 2019 → …

    Activity: Publication peer-review and editorial work typesJournal peer review

    Journal of Combinatorics (Journal)

    David Bevan (Peer reviewer)
    Jan 2018 → …

    Activity: Publication peer-review and editorial work typesJournal peer review