## Newsletter of the Centre for the Mathematics of Symmetry and Computation

It is with deep regret that we have to announce the passing of our colleague and friend Ákos Seress. Ákos lost his brave battle with cancer, and died on February 13, 2013. He had worked with many of us on regular research visits for more than a decade before his ARC Professorial Fellowship allowed him to become a full time member of the CMSC from July 2010. Ákos collaborated with almost all of us, and we miss his friendship and our enthusiastic mathematical interactions with him. There will be numerous joint papers with Ákos Seress appearing for years to come. Our condolences go to Sherry and Laszlo, Ákos's wife and son, also part of our community. (The photo is courtesy of Bogdan Oporowski).

##### New appointments

Luke Morgan will be commencing 10 June 2013 as a Research Associate. Luke will be working with Michael Giudici.

Simon Smith will join the CMSC at the end of June as a Research Associate on an ARC Discovery Early Career Research Award.

##### SymOmega

SymOmega is a mathematical blog run by three CMSC Mathematicians, Michael Giudici, John Bamberg and Gordon Royle.

##### Arxiv

Find in one click all the publications of our members that are deposited on the Arxiv.

##### Conferences

### Dragan Marušič's 60th birthday, Koper, Slovenia, 1-3 May 2013.

Gabriel Verret gave an invited talk "Semiregular automorphisms of arc-transitive graphs". *Website*.

### CSASC 2013, Koper, Slovenia, 9-13 June 2013.

Gabriel Verret will give a talk on "Cayley graphs on abelian groups". *Website*.

### CanaDAM 2013 (Fourth Canadian Conference on Discrete and Algorithmic Mathematics), Memorial University of Newfoundland, Canada, 10-14 June 2013.

Cheryl Praeger will be a plenary speaker, giving a talk entitled "Local transitivity properties of graphs and pairwise transitive designs''. *Website*.

### 2013 PhD Summer School in Discrete Mathematics, Rogla, Slovenia, 16-21 June 2013.

Gabriel Verret will be attending. *Website*.

### The 20th Memorial Amitsur Symposium, Hebrew University, Jerusalem, 17-18 June 2013.

Cheryl Praeger will be a plenary speaker, giving a talk entitled "Coprime actions of finite linear groups''.

### Matroid computation Meeting, La Vacquerie, France, 24-28 June 2013.

Irene Pivotto will be attending.

### Combinatorics, Algebra and More: Peter Cameron's retirement conference, London, England, UK, 8-10 July 2013.

Michael Giudici is an invited speaker. *Website*.

### Banff International Research Station Workshop on Permutation Groups, Canada, 21-26 July 2013.

Alice Devillers, Michael Giudici, Cai Heng Li, Gabriel Verret will be attending. Cheryl Praeger is one of the organisers. *Website*.

### Annual Meeting of the Australian Mathematical Society, 30 September - 3 October 2013, University of Sydney.

John Bamberg will be attending and is organising the session on Group Actions. Cheryl Praeger will be attending too. *Website*.

### Second International Conference on Group Actions and Transitive Graphs, Kunming, Yunnan University, China, September 4-9, 2013.

Cai Heng Li is organising this conference, in honour of Professor Cheryl Praeger's 65th birthday. Registrations are open. *Website*.

### Several CMSC members are very busy organising the 37ACCMCC conference which will be held in Perth 9-13 December 2013.

##### Recent visitors

Padraig O'Cathain, 18-28 February 2013, University of Queensland

Ferdinand Ihringer, 20 February - 4 April 2013, Justus Liebig Universitat

Leonard Scott, 25 February - 3 March 2013, University of Virginia

Jan De Beule, 1 March - 15 April 2013, Universiteit Gent

Tim Burness, 17-31 March 2013, University of Southampton

Andrew Francis, 26-28 March, UWS

Rudi Pendavingh, 7 April - 17 April 2013, Eindhoven

Peter Nelson, 7 April - 17 April 2013, Victoria University, Wellington

Marzieh Akbari, 1 March - 1 October 2013, K.N Toosi University of Technology, Iran

Jon Xu, University of Melbourne, visiting MPhil student cosupervised by John Bamberg

##### Upcoming visitors

Patrick Sole, 21-29 June 2013, CNRS and King AbdulAziz University.

Adel Alahmadi, 26 June - 9 July 2013, King AbdulAziz University.

##### News

The Centre will hold its second annual retreat June 3 to 5 2013. We will be 20 people attending this year (staff, postdocs, visitors, and PhD students), which is a testament to the strong growth of the Centre.

Wei Jin has been awarded a Doctor of Philosophy for his thesis entitled 'Finite s-geodesic transitive graphs'.

PhD students Mark Ioppolo and David Rathiel had their Research proposals approved.

PhD student Dan Hawtin gave his PhD research proposal defence on Tuesday May 7, 2013.

John Bamberg made a presentation to the Indigenous Leadership Seminar on 30 April 2013. The students were in years 11 and 12 and were very enthusiastic!

Cheryl Praeger attended meetings of the Executive Committee for the International Mathematical Union (IMU) March 10-12 in the IMU Offices in Berlin.

Cheryl Praeger gave a Special Colloquium for the Berlin Mathematical School on March 13 at the Urania in Berlin, entitled “Permutations and Polynomial Factorisation”. Prior to this she met with about 20 women PhD students from all mathematical areas and all Berlin universities for a "coffee and cookies" session aimed at encouraging female students to positively consider, and work towards, scientific careers past the doctoral level.

Cheryl Praeger gave an Algebra seminar entitled “Permutations and Polynomial Factorisation” at the University of Cambridge on Wednesday March 20.

Cheryl Praeger gave an Algebra seminar entitled “Edge-transitive oriented graphs of valency four: a global approach“ at King Abdulazziz University, Jeddah, on Monday April 22.

Cheryl Praeger will attend meetings of the Executive Committee for the International Commission for Mathematical Instruction (ICMI) May 21-24 in the IMU Offices in Berlin.

##### Papers

### Published papers

Carmen Amarra, Michael Giudici and Cheryl E. Praeger, Symmetric diameter two graphs with affine-type vertex-quasiprimitive automorphism group, Des. Codes, Cryptogr. 68 (2013) 127-139.

Simeon Ball, John Bamberg, Alice Devillers and Klara Stokes. An alternative way to generalise the pentagon, Journal of Combinatorial Designs 21 (2013), no. 4, 163-179.

John Bamberg, Michael Giudici and Gordon Royle, Hemisystems of small flock quadrangles, Designs, Codes and Cryptography 67 (2013), no. 1, 137-157.

Jing Chen, Cai Heng Li, and Akos Seress, A family of half-transitive graphs, 20 no.1 (2013), Paper 56. Electron. J. Combin.

Silvio Dolfi, R.M. Guralnick, Marcel Herzog and Cheryl E. Praeger, A new solvability criterion for finite groups, J. London Math. Soc. 85 (2012), 269-281.

Neil Gillespie and Cheryl Praeger, Neighbour transitivity on codes in Hamming Graphs, Designs, Codes and Cryptogrpahy, 67 (2013), 385-393.

Neil Gillespie and Cheryl Praeger, Uniqueness of certain completely regular Hadamard Codes, Journal of Combinatorial Theory, Series A, 120 (2013), 1394-1400.

Neil Gillespie, A note on binary completely regular codes with large minimum distance, Discrete Mathematics, 313 (2013), 1532-1534.

Stephen Glasby, Distant parents in complete binary trees, Math. Scientist 38(1) (2013), 1-10.

Simon Guest and Cheryl E. Praeger, Proportions of elements with given 2-part order in the symmetric group, J. Group Theory, 15 (2012), 717-735.

Cai Heng Li, Yanming Wang, Xie Zhu Qing, and Su Ning, Finite groups in which every subgroup is c-normal, Science China Mathematics, 43 (2013), 25-32.

Alice C. Niemeyer, Cheryl E. Praeger and Akos Seress, Estimation problems and randomised group algorithms (Book chapter). In Probabilistic Group Theory, Combinatorics and Computing, Editors: Alla Detinko, Dane Flannery and Eamonn O'Brien. Lecture Notes in Mathematics, Springer, Berlin. 2013. Vol. 2070. Chapter 2, pp.35-82. ISBN: 978-1-4471-4813-5.

Primož Potočnik, Pablo Spiga and Gabriel Verret, On the nullspace of arc-transitive graphs over finite fields, Journal of Algebraic Combinatorics 36 (2012), 389-401.

Primož Potočnik, Pablo Spiga and Gabriel Verret, Cubic vertex-transitive graphs on up to 1280 vertices, Journal of Symbolic Computation 50 (2013), 465-477.

### Accepted Papers

L. Babai, S. Guest, Cheryl E. Praeger and R.A. Wilson, Proportions of r-regular elements in finite classical groups. accepted in J. London Math. Soc.

John Bamberg, Anton Betten, Cheryl E. Praeger and Alfred Wassermann, Unitals int he Desarguesian projective plane of order 16. accepted in J. Stat. Planning and Inference.

Daniela Bubboloni, Cheryl E. Praeger and Pablo Spiga, Normal coverings and pairwise generation of finite alternating and symmetric groups, accepted in J. Algebra.

Neil Gillespie, Dan Hawtin and Cheryl E. Praeger, Elusive codes in Hamming graphs, accepted in Bull. Austral. Math. Soc.

Michael Giudici and Chris Parker, There is no upper bound for the diameter of the commuting graphs of a finite group, accepted in J. Combin. Theory A.

Cai Heng Li and Guang Rao. Self-Complementary vertex-transitive graphs of order a product of two primes, accepted in Bulletin of the Australian Mathematical Society.

Primož Potočnik, Pablo Spiga and Gabriel Verret, On the order of arc-stabilisers in arc-transitive graphs with prescribed local group, accepted in Transactions of the American Mathematical Society.

Gabriel Verret, On the order of arc-stabilisers in arc-transitive graphs, II, accepted in Bulletin of the Australian Math. Society.

### Submitted papers

Andrew P. Bassom, Jennifer Hopwood, J.L. Noakes, Anthony G. Pakes and Cheryl E. Praeger, Advances in mathematics and statistics in Western Australia since 1960.

Silvio Dolfi, R.M. Guralnick, Cheryl E. Praeger and Pablo Spiga. On the maximal number of coprime subdegrees in finite primitive permutation groups.

Simon Guest, Joy Morris, Cheryl E. Praeger and Pablo Spiga. On the maximum orders of elements of finite almost simple groups and primitive permutation groups.

Joseph P.S. Kung, Dillon Mayhew, Irene Pivotto, Gordon F. Royle, Maximum size binary matroids with no AG(3,2)-minor are graphic.

Cai Heng Li, Guang Rao and Shu Jiao Song. On finite self-complementary metacirculants.

Martin Milanič, Anders Sune Pedersen, Daniel Pellicer, Gabriel Verret, Graphs whose complement and square are isomorphic.

Primož Potočnik, Pablo Spiga and Gabriel Verret, Asymptotic enumeration of vertex-transitive graphs of fixed valency.

Pablo Spiga and Gabriel Verret, On intransitive graph-restrictive permutation groups.

Gabriel Verret, Arc-transitive graphs of valency 8 have a semiregular automorphism.