Publications
Some of the following appear on the open preprint server arxiv.org.
- Non-free points for groups generated by a pair of 2 x 2 matrices,
Journal of the London Mathematical Society (2) 62 (2000), 795–801.
- A note on torsion groups generated by pairs of 2 × 2 rational parabolic matrices,
Bulletin of the Australian Mathematical Society 61 (2000), 151–152,
with Grant Cairns.
- The crystallographic restriction, permutations, and Goldbach’s Conjecture,
American Mathematical Monthly 110 (2003), 202–209,
with Grant Cairns and Devin Kilminster.
- Finite permutation groups with a transitive minimal normal subgroup,
Proceedings of the London Mathematical Society (3) 89 (2004), 71–103,
with Cheryl E. Praeger.
- Symplectic spreads,
Designs, Codes and Cryptography 32 (2004), 9–14,
with Simeon Ball, Michel Lavrauw, and Tim Penttila
- Totally Goldbach numbers and related conjectures,
Australian Mathematical Society. Gazette 31 (2004), 251–255,
with David van Golstein Brouwers and Grant Cairns.
- Bounds and quotient actions of innately transitive groups,
Journal of the Australian Mathematical Society 79 (2005), 95–112.
- Transitive eggs,
Innovations in Incidence Geometry 4 (2006), 1–12.
with Tim Penttila.
- Tight sets and m-ovoids of finite polar spaces,
Journal of Combinatorial Theory Series A 114 (2007), no. 7, 1293–1314.
with Shane Kelly, Maska Law, and Tim Penttila.
- Transitive decompositions of graph products: rank 3 product action type,
Journal of Group Theory 11 (2008), no. 2, 185–228.
with Geoffrey Pearce and Cheryl E. Praeger.
- A construction of one-dimensional affine flag-transitive linear spaces,
Finite Fields and their Applications 14 (2008), no. 2, 537-548,
with Michael Pauley.
- Overgroups of cyclic Sylow subgroups of linear groups,
Communications in Algebra 36 (2008), no. 7, 2503–2543,
with Tim Penttila.
- Elation generalised quadrangles for which the number of lines on a point is the successor of a prime,
Journal of the Australian Mathematical Society 85 (2008), no. 3, 289–303,
with Tim Penttila and Csaba Schneider.
- A hemisystem of a nonclassical generalised quadrangle,
Designs, Codes and Cryptography 51 (2009), no. 2, 157–165,
with Frank De Clerck and Nicola Durante.
- A classification of transitive ovoids, spread, and m-systems of polar spaces,
Forum Mathematicum 21 (2009), no. 2, 181–216,
with Tim Penttila.
- Tight sets and m-ovoids of generalised quadrangles,
Combinatorica 29 (2009), no. 1, 1–17,
with Maska Law and Tim Penttila.
- Every flock generalised quadrangle has a hemisystem,
Bulletin of the London Mathematical Society 42 (2010), no. 5, pp. 795–810,
with Michael Giudici and Gordon Royle. arxiv
- A geometric construction of Mathon’s perp-system from four lines of PG(5, 3),
Journal of Combinatorial Designs 18 (2010), no. 6, pp. 450–461,
with Frank De Clerck.
- Point regular groups of automorphisms of generalised quadrangles,
Journal of Combinatorial Theory Series A, 118 (2011), no. 6, pp. 450--461,
with Michael Giudici.
- Intriguing sets of partial quadrangles,
Journal of Combinatorial Designs 19 (2011), no. 3, pp. 217--245,
with Frank De Clerck and Nicola Durante.
- Generalised quadrangles with a group of automorphisms acting primitive on points and lines,
Journal of Combinatorial Theory Series A 119 (2012), no. 7, pp. 1479 -- 1499,
with Michael Giudici, Joy Morris, Gordon Royle and Pablo Spiga.
- Weighted intriguing sets of finite generalised quadrangles,
Journal of Algebraic Combinatorics 36 (2012), no. 1, pp. 149 -- 173,
with Alice Devillers and Jeroen Schillewaert.
- A classification of the strongly regular generalised Johnson graphs,
Annals of Combinatorics 16 (2012), no. 3, pp. 489 -- 506,
with Andrew D. Cannon and Cheryl E. Praeger.
- Low dimensional models of the finite split Cayley hexagon,
Contemporary Mathematics 579 (2012), pp. 1 -- 20,
with Nicola Durante.
- Hemisystems of small flock quadrangles,
Designs, Codes and Cryptography 67 (2013), no. 1, pp. 137 -- 157,
with Michael Giudici and Gordon Royle.
- An alternative way to generalise the pentagon,
Journal of Combinatorial Designs 21 (2013), no. 4, pp. 163 -- 179,
with Simeon Ball, Alice Devillers and Klara Stokes.
- The classification of almost simple 3/2-transitive groups,
Transactions of the American Mathematical Society 365 (2013), no. 8, pp. 4257 -- 4311,
with Michael Giudici, Martin Liebeck, Cheryl Praeger, and Jan Saxl.
- Unitals in the Desarguesian projective plane of order 16,
Journal of Statistical Planning and Inference 144 (2014), pp. 110 -- 122.
with Anton Betten, Cheryl Praeger and Alfred Wasserman.
- Bounds on the diameter of Cayley graphs of the symmetric group,
Journal of Algebraic Combinatorics 40 (2014), no. 1, pp. 1 -- 22.
with Nick Gill, Thomas P. Hayes, Harald A. Helfgott, Ákos Seress and Pablo Spiga.
- Editorial: Special issue on finite geometries in honor of Frank De Clerck,
Designs, Codes and Cryptography 72 (2014), no. 1, pp. 1 -- 5,
with Jan De Beule, Nicola Durante, and Michael Lavrauw.
- AS-configurations and skew-translation generalised quadrangles,
Journal of Algebra (special issue in memory of Ákos Seress) 421 (2015), pp. 311 -- 330.
with S. P. Glasby and Eric Swartz.
- Triple factorisations of the general linear group and their associated geometries,
Linear Algebra and its Applications 469 (2015), pp. 169--203,
with Seyed Hassan Alavi and Cheryl E. Praeger.
- Locally triangular graphs and rectagraphs with symmetry,
Journal of Combinatorial Theory Series A 133 (2015), pp. 1 -- 28,
with Alice Devillers, Joanna B. Fawcett, and Cheryl E. Praeger.
- Completing Segre's proof of Wedderburn's little theorem,
Bulletin of the London Mathematical Society 47 (2015), no. 3, pp. 483 -- 492.
with Tim Penttila.
- An enumeration of certain projective ternary two-weight codes,
Journal of Combinatorial Designs, 24 (2016), no. 1, pp. 21 -- 35,
with Michael Martis and Sylvia Morris.
- Generalised quadrangles and transitive pseudo-hyperovals,
Journal of Combinatorial Designs, 24 (2016), no. 4, pp. 151 -- 164,
with S. P. Glasby, Tomasz Popiel, and Cheryl E. Praeger.
- A note on relative hemisystems of Hermitian generalised quadrangles,
Designs, Codes & Cryptography, 81 (2016), no. 1, pp. 131 -- 144,
with Melissa Lee and Eric Swartz.
- Point-primitive generalised hexagons and octagons,
Journal of Combinatorial Theory Series A, 147 (2017), pp. 186 -- 204,
with S. P. Glasby, Tomasz Popiel, Cheryl Praeger, and Csaba Schneider.
- New non-existence proofs for ovoids of Hermitian polar spaces and hyperbolic quadrics,
Annals of Combinatorics, 21 (2017), no 1, pp. 25 -- 42,
with Jan De Beule and Ferdinand Ihringer.
- Point-primitive, line-transitive generalised quadrangles of holomorph type,
Journal of Group Theory 20 (2017), no. 2, pp. 269 -- 287.
with Tomasz Popiel and Cheryl Praeger.
- A relative m-cover of the Hermitian surface is a relative hemisystem,
Journal of Algebraic Combinatorics 45 (2017), no. 4, pp. 1217 -- 1228.
with Melissa Lee.
- Synchronization and separation in the Johnson schemes,
Portugaliae Mathematica 74 (2017), no. 3, pp. 213 -- 232.
with Mohammed Aljohani and Peter J. Cameron.
- A classification of finite antiflag-transitive generalized quadrangles,
Transactions of the American Mathematical Society 370 (2018), no. 3, pp. 1551 -- 1601,
with Cai-Heng Li and Eric Swartz.
- Bruck nets and partial Sherk planes,
Journal of the Australian Mathematical Society 104 (2018), no. 1, pp. 1 -- 12.
with Joanna B. Fawcett and Jesse Lansdown.
- A new infinite family of hemisystems of the Hermitian surface,
Combinatorica 38 (2018), no. 1, pp. 43 -- 66.
with Melissa Lee, Koji Momihara, Qing Xiang.
- On m-ovoids of regular near polygons,
Designs, Codes & Cryptography 86 (2018), no. 5, pp. 997 -- 1006.
with Jesse Lansdown and Melissa Lee.
- On regular induced subgraphs of bipartite cages,
Journal of Combinatorial Theory Series A 158 (2018), pp. 254 -- 275.
with Anurag Bishnoi and Gordon Royle.
- Maximal linear groups induced on the Frattini quotient of a p-group,
Journal of Pure and Applied Algebra 222 (2018), no. 10, pp. 2931 -- 2951,
with S. P. Glasby, Luke Morgan, and Alice Niemeyer.
- On the circular altitude of a graph,
Australasian Journal of Combinatorics 72 (2018), no. 2, pp. 357 -- 368,
with Brian Corr, Alice Devillers, Daniel Hawtin, Irene Pivotto, and Eric Swartz.
- On abstract ovals with Pascalian secant lines,
Journal of Group Theory 21 (2018), no. 6, 1051 -- 1064,
with Tim Harris and Tim Penttila.
- The covering radii of the 2-transitive unitary, Suzuki, and Ree groups,
Journal of Group Theory 22 (2019), no. 1, 103 -- 117,
with Cheryl E. Praeger and Binzhou Xia.
- Simple groups, product actions, and generalized quadrangles,
Nagoya Mathematical Journal 234 (2019), 87 -- 126.
with Tomasz Popiel and Cheryl Praeger.
- On intriguing sets of the Penttila-Williford association scheme,
Linear Algebra and its Applications 582 (2019), no. 1 (December), 327 -- 345.
with Klaus Metsch.
- Permutations with orders coprime to a given integer,
Electronic Journal of Combinatorics, 27 (2020), #P1.6,
with Stephen Glasby, Scott Harper, Cheryl E. Praeger.
- On \(p\)-groups with automorphism groups related to the Chevalley group \(G_2(p)\),
Journal of the Australian Mathematical Society 108 (2020), no. 3, pp. 321 -- 331.
with Saul D. Freedman and Luke Morgan.
- The thickness of Schubert cells as incidence structures,
Journal of the Australian Mathematical Society 109 (2020), no. 2, pp. 145 -- 156.
with Arun Ram and Jon Xu.
- No almost simple sporadic group acts primitively on the points of a generalised quadrangle,
Discrete Mathematics 344 (2021), no. 4, 112291.
with James Evans.
- A classification of finite locally 2-transitive generalized quadrangles,
Transactions of the American Mathematical Society 374 (2021), no. 3, 1535 -- 1578.
with Cai-Heng Li and Eric Swartz.
To appear
Submitted
- Partial linear spaces with a rank 3 affine primitive group of automorphisms,
with Alice Devillers, Joanna B. Fawcett, Cheryl E. Praeger.
- FinInG: a package for finite incidence geometry,
with Anton Betten, Philippe Cara, Jan De Beule, Max Neunhoeffer, and Michel Lavrauw.
- The minimum degree of minimal Ramsey graphs for cliques,
with Anurag Bishnoi and Thomas Lesgourges.
- Pseudo-ovals of elliptic quadrics as Delsarte designs of association schemes,
with Giusy Monzillo and Alessandro Siciliano.
- Orbits of Sylow subgroups of finite permutation groups,
with Alexander Bors, Alice Devillers, Michael Giudici, Cheryl Praeger, and Gordon Royle.
In preparation
- Vanishing Krein parameters for finite polar spaces,
with Jesse Lansdown.
- Symplectic neighbour-transitive codes in Johnson graphs,
with Alice Devillers, Mark Ioppolo, Cheryl E. Praeger.
- Euclidean geometry is incidence geometry,
with Tim Penttila.
- Simpler foundations for the hyperbolic plane,
with Tim Penttila.
- Ovoids and groups of Lie type, with Arun Ram and Jon Xu.
- On m-ovoids of dual twisted triality hexagons
- Triple factorisations of classical groups by maximal parabolic subgroups and their associated geometries, with Seyed Hassan Alavi and Cheryl E. Praeger.
- On the elation group of the dual of the \(H(4,q^2)\) generalised quadrangle, with Michel Lavrauw and Tim Penttila.
- On the geometry of Kantor, with Nicola Durante.
- Classical geometry I. Real Euclidean and Inversive Geometry, with Tim Penttila [book]
- Classical geometry II. Real Affine Geometry, with Tim Penttila [book]
- Classical geometry III. Real Projective Geometry, with Tim Penttila [book]
- Classical geometry IV. Foundations of Euclidean geometry. with tim Penttila [book]
- Incidence geometry I. Affine and projective geometry over a field. (with Tim Penttila [book]
- Incidence geometry II. Foundations of affine and projective geometry. (with Tim Penttila) [book]
- Incidence geometry III. Finite geometries. (with Tim Penttila) [book]