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.

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.

A structural characterisation of Av(1324) and new bounds on its growth rate (2020-03-25)

Bevan, David; Brignall, Robert; Elvey Price, Andrew and Pantone, Jay

European Journal of Combinatorics, Article 103115 ((In Press))

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)

Well-quasi-ordering and finite distinguishing number (2019)

Atminas, Aistis and Brignall, Robert

Journal of Graph Theory ((Early View))

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)