Robert Brignall

Senior Lecturer in Combinatorics

WELCOME!

I am a Senior Lecturer in Combinatorics in the School of Mathematics and Statistics at The Open University. My research interests primarily focus on the study of infinite antichains, well-quasi-ordering, permutation patterns, and the interplay between permutation patterns and similar concepts in graph theory. You may read more about my research, view my list of publications or my list of talks.

From 2013-2019 I was the School's Director of Research. I am a member of the Edinburgh Mathematical Society Research Committee, and the European Mathematical Society.

Previously, I was a research fellow in the Department of Mathematics at the University of Bristol, and before that I was a PhD student in the School of Mathematics and Statistics at the University of St Andrews.

In the past, I founded the Bristol Combinatorics Seminar, I was on the organising committees for Techniques and Problems in Graph Theory, Permutation Patterns 2010, Permutation Patterns 2011, I chaired the local organising committee for Permutation Patterns 2015, and I was on the programme committee for Permutation Patterns 2019, and I am on the programme committee for Permutation Patterns 2025.

Beyond mathematics, I occasionally sing. I have also created a number of online games, including the somewhat-popular Byrdle.

RESEARCH

My research interests broadly lie in the study of combinatorial and relational structures, in a blend of structural, extremal and enumerative combinatorics. My background is in the study of permutation containment and avoidance, where enumeration is the main game. However, the structural study of permutations can often be translated to other combinatorial objects, most notably graphs, where the consequences can be wide-ranging. Currently, I am especially investigating the question of well-quasi-ordering in combinatorial objects and the corresponding construction of infinite antichains, but I also have ongoing projects in permutation enumeration, structural graph theory, and graph parameters.

I submitted my PhD Thesis, entitled "Simplicity in Relational Structures and its Application to Permutation Classes", in July 2007, and successfully defended it in October 2007. My external examiner was Einar Steingrímsson (Strathclyde University), my internal Steve Linton. My PhD was written whilst in the School of Mathematics and Statistics at the University of St Andrews, was supervised by Prof Nikola Ruškuc, and was funded by EPSRC.

Research students

  • Aditi Krishnakumar (2025-) [second supervisor]
  • Ben Jarvis (2021-)
  • Dan Cocks (2020-2024) [Thesis]
  • Kirstie Asciak (2018-2024) [second supervisor, part time]
  • Olivia Jeans (2017-2023) [second supervisor, part time]
  • James Tuite (2015-2021) [second supervisor]
  • David Marchant (2016-2020) [part time] [Thesis]
  • James Fraser (2016-2019) [second supervisor]
  • Jakub Sliacan (2015-2018). [Thesis]
  • David Bevan (2012-2015). [Thesis]

Conference Organisation

  • Programme Committee, Permutation Patterns 2025, University of St Andrews, UK, 7-11 July 2025.
  • Programme Committee, Permutation Patterns 2019, Universität Zürich, Switzerland, 17-21 June 2019.
  • Local organising committee, Winter Combinatorics Meeting, Open University, annually 2011-2016.
  • Chair of Local Organising Committee, Permutation Patterns 2015, De Morgan House, London, 15-19 June 2015.
  • Organising Committee, Permutation Patterns 2011, California Polytechnic University, San Luis Obispo, USA, 20-24 June 2011.
  • Organising Committee, Permutation Patterns 2010, Dartmouth College, USA, 9-13 August 2010.
  • Local organising committee, Techniques and Problems in Graph Theory, University of Bristol, 1-3 July 2009.

Editing

Other Activities

  • Review for the LMS Newsletter of Alex's Adventures in Numberland by Alex Bellos. [PDF] [Newsletter]
    A version also appeared in Plus Magazine. [Plus]
  • Read my MathSciNet Reviews.
  • Referee for: Annals of Combinatorics, Discrete Applied Mathematics, Discrete Mathematics, Electronic Journal of Combinatorics, Graphs and Combinatorics, Journal of Combinatorial Theory Series A, Journal of Combinatorics, LMS Lecture Note Series, Mathematika, Pure Mathematics and Applications.

List of Coauthors

PUBLICATIONS

Submitted Papers

    Journal articles

      Conference paper

        Theses

        • Brignall, R., Pattern classes of permutations: constructions, atomicity and the finite basis property, M.Sc. Thesis, September 2004. [PDF]
        • Brignall, R., Simplicity in Relational Structures and its Application to Permutation Classes, Ph.D. Thesis, October 2007. [PDF]

        TALKS

        Invited Talks

        Contributed Talks

        CONTACT

        Address

        School of Mathematics and Statistics, The Open University, Milton Keynes, MK7 6AA

        Email

        Before "no spam pleaserbrignall.org.uk", add "robert"

        This page last modified on 4 April 2025.