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Dr Robert Brignall

Profile summary

Professional biography

I'm a Senior Lecturer in Combinatorics in the School of Mathematics and Statistics, having joined the OU as a Lecturer in 2010. After graduating from the University of Cambridge in 2003, I studied first for an MSc and then completed my PhD in 2007 at the University of St Andrews, before moving to the University of Bristol as a Research Fellow.  You should visit my personal page if you would like to read more.

Research interests

My research interests lie in enumerative and structural combinatorics, more specifically on permutation patterns, graph theory, and well-quasi-ordering. You should visit my personal page if you would like to read more, including access to my preprints, papers, and slides of talks that I have given.

Externally funded projects

LMS Grant Award
RoleStart dateEnd dateFunding source
Lead01 Oct 201630 Sep 2017LMS London Mathematical Society

LMS Research Scheme Grant - Grant reference: 11579 - Title of Conference: Mathematics in the regions: Staff Tutor Research Grant for Conference to be held in October 2016

Publications

Labelled Well-Quasi-Order in Juxtapositions of Permutation Classes (2024)
Brignall, Robert
The Electronic Journal of Combinatorics, 31, Article P2.21(2)


A framework for minimal hereditary classes of graphs of unbounded clique-width (2023)
Brignall, Robert and Cocks, Daniel
SIAM Journal on Discrete Mathematics, 37(4) (pp. 2558-2584)


Uncountably Many Minimal Hereditary Classes of Graphs of Unbounded Clique-Width (2022-03-25)
Brignall, Robert and Cocks, Daniel
Electronic Journal of Combinatorics, 29, Article P1.63(1)


Labelled well-quasi-order for permutation classes (2022)
Brignall, Robert and Vatter, Vincent
Combinatorial Theory, 2(3)


Minimal classes of graphs of unbounded clique-width defined by finitely many forbidden induced subgraphs (2021-05-31)
Atminas, A.; Brignall, R.; Lozin, V. and Stacho, J.
Discrete Applied Mathematics, 295 (pp. 57-69)


Well-quasi-ordering and finite distinguishing number (2020-09)
Atminas, Aistis and Brignall, Robert
Journal of Graph Theory, 95(1) (pp. 5-26)


A structural characterisation of Av(1324) and new bounds on its growth rate (2020-08)
Bevan, David; Brignall, Robert; Elvey Price, Andrew and Pantone, Jay
European Journal of Combinatorics, 88, Article 103115


Combinatorial specifications for juxtapositions of permutation classes (2019-10-11)
Brignall, Robert and Sliacan, Jakub
Electronic Journal of Combinatorics, 26, Article P4.4(4)


Rationality for subclasses of 321-avoiding permutations (2019-05)
Albert, Michael; Brignall, Robert; Ruskuc, Nik and Vatter, Vincent
European Journal of Combinatorics, 78 (pp. 44-72)


Deciding whether there are infinitely many prime graphs with forbidden induced subgraphs (2019-03-31)
Brignall, Robert; Choi, Hojin; Jeong, Jisu and Oum, Sang-il
Discrete Applied Mathematics, 257 (pp. 60-66)


Zeros of the Möbius function of permutations (2019)
Brignall, Robert; Jelínek, Vít; Kynčl, Jan and Marchant, David
Mathematika, 65(4) (pp. 1074-1092)


A Counterexample Regarding Labelled Well-Quasi-Ordering (2018-11)
Brignall, Robert; Engen, Michael and Vatter, Vincent
Graphs and Combinatorics, 34(6) (pp. 1395-1409)


Characterising inflations of monotone grid classes of permutations (2018-02)
Albert, Michael; Atminas, Aistis and Brignall, Robert
Journal of Combinatorial Theory, Series A, 154 (pp. 444-463)


The Möbius function of permutations with an indecomposable lower bound (2018)
Brignall, Robert and Marchant, David William
Discrete Mathematics, 341(5) (pp. 1380-1391)


Linear Clique-Width for Hereditary Classes of Cographs (2017-04)
Brignall, Robert; Korpelainen, Nicholas and Vatter, Vincent
Journal of Graph Theory, 84(4) (pp. 501-511)


Juxtaposing Catalan Permutation Classes with Monotone Ones (2017)
Brignall, Robert and Sliacan, Jakub
Electronic Journal of Combinatorics, 24, Article 2.11(2)


2×2 monotone grid classes are finitely based (2016-11-02)
Albert, Michael and Brignall, Robert
Discrete Mathematics & Theoretical Computer Science, 18, Article 1(2)


Bichain graphs: geometric model and universal graphs (2016-01-30)
Brignall, Robert; Lozin, Vadim V. and Stacho, Juraj
Discrete Applied Mathematics, 199 (pp. 16-29)


Well-Quasi-Order for Permutation Graphs Omitting a Path and a Clique (2015-04-29)
Atminas, Aistis; Brignall, Robert; Korpelainen, Nicholas; Lozin, Vadim and Vatter, Vincent
Electronic Journal of Combinatorics, 22, Article P2.20(2)


A simple proof of a theorem of Schmerl and Trotter for permutations (2015)
Brignall, Robert and Vatter, Vincent
Journal of Combinatorics, 6(1–2) (pp. 47-54)


Enumerating indices of Schubert varieties defined by inclusions (2014-04-30)
Albert, Michael H. and Brignall, Robert
Journal of Combinatorial Theory, Series A, 123(1) (pp. 154-168)


Large infinite antichains of permutations (2013)
Albert, Michael; Brignall, Robert and Vatter, Vincent
Pure Mathematics and Applications, 24(2) (pp. 47-57)


The enumeration of three pattern classes using monotone grid classes (2012-08-16)
Albert, M. H.; Atkinson, M. D. and Brignall, Robert
Electronic Journal of Combinatorics, 19(3) (P20)


Grid classes and partial well order (2012-01)
Brignall, Robert
Journal of Combinatorial Theory, Series A, 119(1) (pp. 99-116)


Modular decomposition and the reconstruction conjecture (2012)
Brignall, Robert; Georgiou, Nicholas and Waters, Robert J.
Journal of Combinatorics, 3(1) (pp. 123-134)


Simple extensions of combinatorial structures (2011-07)
Brignall, Robert; Ruškuc, Nik and Vatter, Vincent
Mathematika, 57(2) (pp. 193-214)


The enumeration of permutations avoiding 2143 and 4231 (2011)
Albert, M. H.; Atkinson, M. D. and Brignall, Robert
Pure Mathematics and Applications, 22(2) (pp. 87-98)


Growth rates for subclasses of Av(321) (2010-10-22)
Albert, M. H.; Atkinson, M. D.; Brignall, R.; Ruškuc, N.; Smith, Rebecca and West, J.
Electronic Journal of Combinatorics, 17(1) (R141)


Almost avoiding permutations (2009)
Brignall, Robert; Ekhad, Shalosh B.; Smith, Rebecca and Vatter, Vincent
Discrete Mathematics, 309(23-24) (pp. 6626-6631)


Decomposing simple permutations, with enumerative consequences (2008-07)
Brignall, Robert; Huczynska, Sophie and Vatter, Vincent
Combinatorica, 28(4) (pp. 385-400)


Simple permutations and algebraic generating functions (2008-04)
Brignall, Robert; Huczynska, Sophie and Vatter, Vincent
Journal of Combinatorial Theory, Series A, 115(3) (pp. 423-441)


Simple permutations: Decidability and unavoidable substructures (2008-02-04)
Brignall, Robert; Ruškuc, Nik and Vatter, Vincent
Theoretical Computer Science, 391(1-2) (pp. 150-163)


Wreath products of permutation classes (2007)
Brignall, Robert
Electronic Journal of Combinatorics, 14(1) (Research Paper 46, 15 pp. (electronic))


Permutation classes of polynomial growth (2007)
Albert, M. H.; Atkinson, M. D. and Brignall, Robert
Annals of Combinatorics, 11(3-4) (pp. 249-264)


A survey of simple permutations (2010)
Brignall, Robert
In: Linton, Steve; Ruškuc, Nik and Vatter, Vincent eds. Permutation Patterns. London Mathematical Society Lecture Notes Series (376) (pp. 41-65)
ISBN : 9780521728348 | Publisher : Cambridge University Press | Published : Cambridge, UK


Staircases, dominoes, and the growth rate of 1324-avoiders (2017-08-03)
Bevan, David; Brignall, Robert; Price, Andrew Elvey and Pantone, Jay
In : The European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB'17) (Aug 28 - - Sep 1 2017, Vienna) (pp. 123-129)