Topics  Some of my
publications 
Finite Abelian groups and their duals 
R. A. Bailey:
Patterns of confounding in factorial designs.
Biometrika
64
(1977),
597–603.
[Maths Reviews 0501643 (58 #18945)]
R. A. Bailey:
Dual Abelian groups in the design of experiments.
In Algebraic Structures and Applications
(eds. P. Schultz, C. E. Praeger and R. P. Sullivan),
Marcel Dekker, New York,
1982,
pp. 45–54.
[Maths Reviews 0647165 (83m: 62135)]
R. A. Bailey:
Factorial design and Abelian groups.
Linear Algebra and its Applications
70
(1985),
349–368.
[Maths Reviews 0808552 (87c: 62151)]
R. A. Bailey:
Cyclic designs and factorial designs.
In Probability, Statistics and Design of Experiments
(proceedings of the R. C. Bose Symposium on
Probability, Statistics and Design of Experiments, Delhi, 27–30
December, 1988)
(ed. R. R. Bahadur),
Wiley Eastern, New Delhi,
1990,
pp. 51–74.

Which combinatorial objects have a group of automorphisms whose
permutation character is multiplicityfree? 
R. A. Bailey:
Latin squares with highly transitive automorphism groups.
Journal of the Australian Mathematical Society, Series A
33
(1982),
18–22.
[Maths Reviews 0662355 (83g: 05021)]
R. A. Bailey, Cheryl E. Praeger, C. A. Rowley and T. P. Speed:
Generalized wreath products of permutation groups.
Proceedings of the London Mathematical Society
47
(1983),
69–82.
[Maths Reviews 0698928 (85b: 20005)]
P. P. Alejandro, R. A. Bailey and P. J. Cameron:
Association schemes and permutation groups.
Discrete Mathematics
266
(2003),
47–67.
doi:10.1016/S0012365X(02)007987
[Maths Reviews 1991706 (2004c: 05216)]

What are useful ways of generalizing the direct and wreath products as
methods of combining permutation groups? 
R. A. Bailey, Cheryl E. Praeger, C. A. Rowley and T. P. Speed:
Generalized wreath products of permutation groups.
Proceedings of the London Mathematical Society
47
(1983),
69–82.
[Maths Reviews 0698928 (85b: 20005)]
R. A. Bailey and Peter J. Cameron:
Crested products of association schemes.
Journal of the London Mathematical Society
72
(2005),
1–24.
doi: 10.1112/S0024610705006666
[Maths Reviews 2145725 (2006h: 05240)]

Which finite groups have terraces? 
R. A. Bailey:
Quasicomplete Latin squares: construction and randomization.
Journal of the Royal Statistical Society, Series B
46
(1984),
323–334.
[Maths Reviews 0781893 (86i: 62161)]
R. A. Bailey and Cheryl E. Praeger:
Directed terraces for direct product groups.
Ars Combinatoria
25A
(1988),
73–76.
[Maths Reviews 0942492 (89i: 20041)]
Ian Anderson and R. A. Bailey:
Completeness properties of conjugates of Latin squares based on
groups, and an application to bipartite tournaments.
Bulletin of the Institute of Combinatorics and its Applications
21
(1997),
95–99.
[Maths Reviews 1470311 (98d: 05032)]

What can we learn about a design from its automorphism group? 
R. A. Bailey:
Contribution to the discussion of
`Symmetry models and hypotheses for structured data layouts' by A. P. Dawid.
Journal of the Royal Statistical Society, Series B
50
(1988),
pp. 22–24.
R. A. Bailey:
Automorphism groups of block structures with and without treatments.
In Coding Theory and Design Theory. Part II: Design Theory
(ed. D. RayChaudhuri),
IMA Volumes in Mathematics and its Applications,
21,
SpringerVerlag, New York,
1990,
pp. 24–41.
[Maths Reviews 1056523 (91g: 05011)]
R. A. Bailey and C. A. Rowley:
General balance and treatment permutations.
Linear Algebra and its Applications
127
(1990),
183–225.
[Maths Reviews 1048802 (91d: 05014)]
R. A. Bailey:
Contribution to the discussion of
`Invariance and factorial models' by P. McCullagh.
Journal of the Royal Statistical Society, Series B
62
(2000),
pp. 239–241.

Automorphism groups of combinatorial structures 
R. A. Bailey:
Distributive block structures and their automorphisms.
In Combinatorial Mathematics VIII
(ed. K. L. McAvaney),
Lecture Notes in Mathematics,
884
SpringerVerlag, Berlin,
1981,
pp. 115–124.
[Maths Reviews 0641241 (83c: 62119)]
R. A. Bailey:
Latin squares with highly transitive automorphism groups.
Journal of the Australian Mathematical Society, Series A
33
(1982),
18–22.
[Maths Reviews 0662355 (83g: 05021)]
R. A. Bailey and D. Jungnickel:
Translation nets and fixedpointfree group automorphisms.
Journal of Combinatorial Theory, Series A
55
(1990),
1–13.
[Maths Reviews 1070011 (91h: 05030)]
R. A. Bailey:
A Howell design admitting A_{5}.
Discrete Mathematics
167168
(1997),
65–71.
[Maths Reviews 1446733 (98h: 05039)]
Ian Anderson and R. A. Bailey:
Completeness properties of conjugates of Latin squares based on
groups, and an application to bipartite tournaments.
Bulletin of the Institute of Combinatorics and its Applications
21
(1997),
95–99.
[Maths Reviews 1470311 (98d: 05032)]
R. A. Bailey, M. Buratti, G. Rinaldi and T. Traetta:
On 2pyramidal Hamiltonian cycle systems.
Bulletin of the Belgian Mathematical Society—Simon Stevin,
21
(2014),
747–758.

Statistical models invariant under a group of permutations 
R. A. Bailey:
Contribution to the discussion of
`Symmetry models and hypotheses for structured data layouts' by A. P. Dawid.
Journal of the Royal Statistical Society, Series B
50
(1988),
pp. 2224.
R. A. Bailey:
Contribution to the discussion of
`Invariance and factorial models' by P. McCullagh.
Journal of the Royal Statistical Society, Series B
62
(2000),
pp. 239241.
R. A. Bailey, Persi Diaconis, Daniel N. Rockmore and Chris Rowley:
A spectral analysis approach for experimental designs.
In Excursions in Harmonic Analysis, Volume 4
(eds. R. Balan, M. Begué, J. J. Benedetto, W. Czaja and K. A. Okoudjou),
Springer International Publishing (2015), pp. 367–395.
doi: 10.1007/9783319201887_14

Groups generated by derangements 
R. A. Bailey, Peter J. Cameron, Michael Giudici and Gordon Royle:
Groups generated by derangements.
Journal of Algebra, 572 (2021), 245–262.
doi: 10.1016/j.jalgebra.2020.12.020
