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.

I organise our Seminar Series. From 2013-2019 I was the School's Director of Research. I am a member of the Edinburgh Mathematical Society 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 program committee for Permutation Patterns 2019.

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

Grants

In Opinion 117, Doron Zeilberger (my academic grandfather!) suggested more people should upload grant bids, so here are some older ones of mine.
  • [FUNDED] EPSRC First Grant, EP/J006130/1, £91,797, 1st October 2012 -- 30th September 2013. Infinite Antichains of Combinatorial Structures.
    [Proposal] [GoW]
  • [FUNDED] LMS Conference Grants (Scheme 1), £560, 30th January 2013. Winter Combinatorics Meeting, held at The Open University.
    [Proposal].
  • [NOT FUNDED] ERC Starting Grant, 2014. [Part B2]
  • [FUNDED] LMS Conference Grants (Scheme 1), £2,000, 11th--12th September 2014. Valediction to Jeremy Gray, held at Mercure Parkside Hotel, Milton Keynes.
    [Proposal].
  • [FUNDED] LMS Conference Grants (Scheme 1), £1,908, 15th--19th June 2015. Permutation Patterns 2015, held at De Morgan House, London.
    [Proposal].
  • [NOT FUNDED] EPSRC Standard Grant, 2015. [Proposal]

Conference Organisation

  • Program 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

  1. Brignall, R., Labelled well-quasi-order in juxtapositions of permutation classes.
    [PDF] [BibTeX] [Abstract]
  2. Brignall, R., and Vatter, V., Uncountably many enumerations of well-quasi-ordered permutation classes.
    [PDF] [BibTeX] [Abstract]

Journal articles

  1. Brignall, R., and Cocks, D., A framework for minimal hereditary classes of graphs of unbounded clique-width. SIAM Journal on Discrete Mathematics 37(4) (2023), 2558-84.
    [PDF] [Journal] [BibTeX] [Abstract]
  2. Brignall, R., and Vatter, V., Labeled well-quasi-order for permutation classes. Combinatorial Theory 2(3) (2022), #14 (55pp).
    [PDF] [Journal] [BibTeX] [Abstract]
  3. Brignall, R., and Cocks, D., Uncountably many minimal hereditary classes of graphs of unbounded clique-width. Electronic Journal of Combinatorics, 29(1) (2022), #P1.63 (27pp)
    [PDF] [Journal] [BibTeX] [Abstract]
  4. Atminas, A., Brignall, R., Lozin, V., and Stacho, J., Minimal classes of graphs of unbounded clique-width defined by finitely many forbidden induced subgraphs. Discrete Applied Mathematics 295 (2021), 57-69.
    [PDF] [Journal] [BibTeX] [Abstract]
  5. Atminas, A., and Brignall, R., Well-quasi-ordering and finite distinguishing number. Journal of Graph Theory, 95(1) (2020), 5-26.
    [PDF] [Journal] [BibTeX] [Abstract]
  6. Bevan, D., Brignall, R., Elvey Price, A., and Pantone, J., A structural characterisation of Av(1324) and new bounds on its growth rate. European Journal of Combinatorics, 88 (2020), article 103115.
    [PDF] [Journal] [BibTeX] [Abstract]
  7. Brignall, R., and Sliačan, J., Combinatorial specifications for juxtapositions of permutation classes. Electronic Journal of Combinatorics, 26(4) (2019), #P4.4 (24pp)
    [PDF] [Journal] [BibTeX] [Abstract]
  8. Brignall, R., Jelínek, V., Kynčl, J., and Marchant, D., Zeros of the Möbius function of permutations. Mathematika, 65 (2019), 1074-1092.
    [PDF] [Journal] [BibTeX] [Abstract]
  9. Brignall, R., Choi, H., Jeong, J., and Oum, S.-i., Deciding whether there are infinitely many prime graphs with forbidden induced subgraphs. Discrete Applied Mathematics, 257 (2019), 60-66.
    [PDF] [Journal] [BibTeX] [Abstract]
  10. Albert, M.H., Brignall, R., Ruškuc, N., and Vatter, V., Rationality for subclasses of 321-avoiding permutations. European Journal of Combinatorics, 78 (2019), 44-72.
    [PDF] [Journal] [BibTeX] [Abstract]
  11. Brignall, R., Engen, M., and Vatter, V., A counterexample regarding labelled-well-quasi-ordering. Graphs and Combinatorics, 34 (6) (2018), 1395-1409.
    [PDF] [Journal] [BibTeX] [Abstract]
  12. Brignall, R., and Marchant, D., The Möbius function of permutations with an indecomposable lower bound. Discrete Mathematics, 341(5) (2018), 1380-1391.
    [PDF] [Journal] [BibTeX] [Abstract]
  13. Albert, M.H., Atminas, A., and Brignall, R., Characterising inflations of monotone grid classes of permutations. Journal of Combinatorial Theory, Series A, 154 (2018), 444-463.
    [PDF] [Journal] [BibTeX] [Abstract]
  14. Brignall, R., and Sliačan, J., Juxtaposing Catalan permutation classes with monotone ones. Electronic Journal of Combinatorics, 24(2) (2017), #P2.11 (16pp)
    [PDF] [Journal] [BibTeX] [Abstract]
  15. Brignall, R., Korpelainen, N., and Vatter, V., Linear clique-width for hereditary classes of cographs. Journal of Graph Theory, 84 (2017), 501-511.
    [PDF] [Journal] [BibTeX] [Abstract]
  16. Albert, M.H., and Brignall, R., \(2\times 2\) monotone grid classes are finitely based. Discrete Mathematics and Theoretical Computer Science, 18(2), 2016, #1 (Permutation Patterns 2015)
    [PDF] [Journal] [BibTeX] [Abstract]
  17. Brignall, R., Lozin, V., and Stacho, J., Bichain graphs: geometric model and universal graphs. Discrete Applied Mathematics, 199 (2016), 16-29
    [PDF] [Journal] [BibTeX] [Abstract]
  18. Atminas, A., Brignall, R., Korpelainen, N., Lozin, V., and Vatter, V., Well-quasi-order for permutation graphs omitting a path and a clique. Electronic Journal of Combinatorics 22(2) (2015), #P2.20 (21pp)
    [PDF] [Journal] [BibTeX] [Abstract]
  19. Brignall, R., and Vatter, V., A simple proof of a theorem of Schmerl and Trotter for permutations. Journal of Combinatorics, 6 (2015) No. 1-2, 47-54
    [PDF] [Journal] [BibTeX] [Abstract]
  20. Albert, M.H., and Brignall, R., Enumerating indices of Schubert varieties defined by inclusions. Journal of Combinatorial Theory, Series A, 123 (2014), 154-168
    [PDF] [Journal] [BibTeX] [Abstract]
  21. Albert, M.H., Brignall, R., and Vatter, V., Large infinite antichains of permutations. Pure Mathematics and Applications, 24 (2013) No. 2, 47-57
    [PDF] [BibTeX] [Abstract]
  22. Brignall, R., Georgiou, N., and Waters, R., Modular decomposition and the reconstruction conjecture. Journal of Combinatorics, 3 (2012), 123-134
    [PDF] [Journal] [BibTeX] [Abstract]
  23. Albert, M.H., Atkinson, M.D., and Brignall, R., The enumeration of three pattern classes using monotone grid classes. Electronic Journal of Combinatorics 19(3) (2012), #P20 (34pp)
    [PDF] [Journal] [BibTeX] [Abstract]
  24. Brignall, R., Grid classes and partial well order. Journal of Combinatorial Theory Series A, 119 (2012), 99-116
    [PDF] [Journal] [BibTeX] [Abstract]
  25. Albert, M.H., Atkinson, M.D., and Brignall, R., The enumeration of permutations avoiding 2143 and 4231. Pure Mathematics and Applications, 22 (2011) No. 2, 87-98
    [PDF] [BibTeX] [Abstract]
  26. Brignall, R., Ruškuc, N., and Vatter, V., Simple extensions of combinatorial structures. Mathematika, 57 (2011), 193-214
    [PDF] [Journal] [BibTeX] [Abstract]
  27. Albert, M.H., Atkinson, M.D., Brignall, R., Ruškuc, N., Smith, R., and West, J., Growth rates for subclasses of Av(321). Electronic Journal of Combinatorics 17(1) (2010), #R141 (16pp)
    [PDF] [Journal] [BibTeX] [Abstract]
  28. Brignall, R., A survey of simple permutations. S. Linton, N. Ruškuc and V. Vatter, Eds., vol. 376 of London Mathematical Society Lecture Note Series, Cambridge University Press, pp. 41-65
    [PDF] [Book] [BibTeX] [Abstract]
  29. Brignall, R., Ekhad, S.B., Smith, R., and Vatter, V., Almost avoiding permutations. Discrete Mathematics 309 (2009), 6626-6631
    [PDF] [Journal] [BibTeX] [Abstract]
  30. Brignall, R., Huczynska, S., and Vatter, V., Decomposing simple permutations, with enumerative consequences. Combinatorica, 28 (4) (2008) 385-400
    [PDF] [Journal] [BibTeX] [Abstract]
  31. Brignall, R., Huczynska, S., and Vatter, V., Simple permutations and algebraic generating functions. Journal of Combinatorial Theory Series A 115 (2008), 423-441
    [PDF] [Journal] [BibTeX] [Abstract]
  32. Brignall, R., Ruškuc, N., and Vatter, V., Simple permutations: decidability and unavoidable substructures. Theoretical Computer Science 391 (2008), 150-163
    [PDF] [Journal] [BibTeX] [Abstract]
  33. Albert, M.H., Atkinson, M.D., and Brignall, R., Permutation classes of polynomial growth. Annals of Combinatorics 11 (2007), no. 3-4, 249--264
    [PDF] [Journal] [BibTeX] [Abstract]
  34. Brignall, R., Wreath products of permutation classes. Electronic Journal of Combinatorics 14 (2007), #R46 (15pp)
    [PDF] [Journal] [BibTeX] [Abstract]

Conference paper

  1. Bevan, D., Brignall, R., Elvey Price, A., and Pantone, J., Staircases, dominoes, and the growth rate of 1324-avoiders. Electronic Notes in Discrete Mathematics, 61 (August 2017), 123-129.
    [PDF] [Journal] [BibTeX] [Abstract]

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

Note: Due to the current COVID-19 restrictions I am unable to retrieve any mail from the OU campus.

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

Email

Before "no spam pleaseopen.ac.uk", add "Firstname.Lastname"

This page last modified on 01 June 2023 at 16:07. [Disclaimer]