Centre for the Mathematics of Symmetry and Computation

Newsletter, January 2014

January 2014 newsletter of the Centre for the Mathematics of Symmetry and Computation

The Centre for the Mathematics of Symmetry and Computation is a Centre located within the UWA School of Mathematics and Statistics. We provide a focus for mathematical research and research training in the areas of group theory, combinatorics and computation, to give mathematics the increased visibility it deserves.


Recent and upcoming visitors

  • Jin-Xin Zhou, Beijing Jiaotong University, China, 16 November 2013 – 16 November 2014.
  • Florian Lehner, Graz University of Technology, Austria, 6-29 December 2013. 
  • Dugald MacPherson, University of Leeds, UK, 7-28 February 2014.
  • Pablo Spiga, University of Milano-Bicocca, Italy, March - April 2014. 
  • Many of the participants for ACCMCC came earlier and stayed after the conference.


  • Many members of the CMSC were involved in the WA Junior Maths Olympiad that was held at UWA on 2 November 2013. There were 414 students from 37 schools.
  • John Bamberg ran two 2.5 hour sessions on Codes and Cryptography for the National Youth Science Forum (for beginning year 12 students from all over Australia). 9 January 2014.
  • Alice Devillers, Michael Giudici and Joanna Fawcett were involved in giving a few sessions each for the Science Experience. 14-16 January 2014.
  • Cheryl Praeger resigned from the Council of University Hall (previously Currie Hall) after 23 years of service as Vice Chancellor's nominee.

Other news

  • In February, the CMSC, together with one international guest, will get away to the Perth hills for their third annual retreat. We will work together on problems, getting to know members of the Centre who we are not usually working with. For the first time a mini lecture series will be organised too. There will also certainly be some soccer, some pool and some board game action, during evening and breaks. 
  • John Bamberg  became a managing editor for the  Australasian Journal of Combinatorics.
  • Juliet Burridge completed her honours project Elusive Groups, supervised by Michael Giudici.
  • Brian Corr was awarded his PhD, with thesis Estimation and Computation with Matrices over Finite Fields, supervised by Cheryl Praeger and Ákos Seress.
  • Brian Corr was awarded an Australian Mathematical Society Lift-Off Fellowship.
  • Brian Corr has accepted a research fellowship at the Universidade Federal de Minas Gerais, Belo Horizonte, Brazil.
  • Stephen Glasby joined the editorial board of Communications in Mathematics.
  • Stephen Glasby was appointed as an Adjunct Professor within the School of Mathematics and Statistics starting in April.
  • Cheryl Praeger was awarded the 2013 Thomas Ranken Lyle Medal for her outstanding research accomplishments.
  • Cheryl Praeger has been elected Foreign Secretary of the Australian Academy of Science; the position runs for four years from June 2014.
  • Gordon Royle joined the editorial board of the Electronic Journal of Combinatorics.
  • Blake Segler completed his joint Maths/Physics honours project On the implementation and application of quantum error correction codes, supervised by John Bamberg and Jing-Bo Wang.


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


Representation Theory in Geometry, Topology and Combinatorics, Melbourne, Australia, 4-7 November 2013.

John Bamberg and Alice Devillers gave talks, Guang Rao attended.

The 37th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, Perth, Australia, 9-13 December 2013.

The organising comitee was composed of members of the CMSC, led by Gordon Royle. His report on the conference is in the next section.

Joint Mathematics Meetings of the American Mathematical Society and Mathematical Society of America, Baltimore, USA, 15-18 January 2014.

Eric Swartz gave a talk.

Graphs, Hypergraphs and Computing, Program at Institut Mittag-Leffler, Stockholm, Sweden, January-June 2014.

Gordon Royle is an invited participant for 13 April - 14 May 2014.

Groups, Computation and Geometry, Fort Collins, USA, 9-13 June 2014.

John Bamberg is an invited speaker.

Algebraic Combinatorics: Spectral Graph Theory, Erdös-Ko-Rado Theorems and Quantum Information Theory, A Conference to celebrate the work of Chris Godsil, Waterloo, Canada, 23-27 June 2014.

Cheryl Praeger and Gordon Royle are invited speakers.

Symmetries of Graphs and Networks IV, Rogla, Slovenia, 29 June-5 July 2014.

Michael Giudici and Cai Heng Li are invited speakers.

SIGMAP 2014 WorkshopSymmetry In Graphs, Maps And Polytopes, West Malvern, U.K., 7-11 July 2014.

Cai Heng Li is an invited speaker.

GAGTA 8 (Geometric and Asymptotic Group Theory with Applications), Newcastle, Australia, 21-25 July 2014.

Simon Smith is an organiser.

37th ACCMCC Organiser's report, by Gordon Royle

The 37th Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, which is the annual Australian combinatorics conference, was held at UWA in December 2013 and was deemed a great success. The final total of 106 registered participants was significantly higher than anticipated, and marked the third consecutive time that attendance exceeded 100.

With eight plenary talks (Matt DeVos, Vida Dujmović, Graham Farr, Bill Martin, Dillon Mayhew, Primož Potočnik, Tamás Szőnyi, Nick Wormald) and 86 contributed talks in three parallel sessions, it was often a difficult choice to decide which to attend, and each day was a full one.

We aimed to have at least one group / social activity on every evening, in addition to the “Pub of the Day” every night. These events included the welcome reception on Sunday evening, swimming and fish-n-chips at Cottesloe on Monday, a soccer match on Tuesday, a continuation of the excursion on Wednesday, the conference dinner on Thursday and the Survivors Party on Friday. All were well attended, ran very smoothly and and were very well received, with a particular highlight being the superb food and drink at the University Club for the conference dinner.

The Monadelphous ILC proved to be an ideal conference centre venue, being located very close to the talks, having ample space for delegates to work, rest or socialise between talks or during the long lunch breaks. Easy access to kitchen facilities and the rental of a high-quality automatic coffee machine allowed us to supply continuous refreshments for the delegates. The coffee machine was a particular hit, with exactly 499 coffees being consumed over the week, often while perusing the daily newsletter “The Daily Combinatorialist”.

Over the course of the week, and subsequently, I’ve had numerous people remarking on how much they enjoyed the conference, how well everything went, and how well organised everything was. But  of course, none of this happens without two things - money and a significant effort behind the scenes. For the former we were enormously helped by Head of School, Andrew Bassom who gave us money from his Head’s fund, and by Eric and Irene who wrote an application for a Faculty Research Grant. For the latter, I was immensely helped by the large number of CMSC members, who each undertook one or more tasks and did them brilliantly with no fuss.

In particular, I’d like to thank (alphabetical, organising committee first):
  • John Bamberg, Organising Committee, Web site, Program booklet, Welcome bag (T-shirt)
  • Alice Devillers, Organising Committee, Treasurer
  • Michael Giudici, Organising Committee, Accommodation, Program schedule
  • Irene Pivotto, Organising Committee, Faculty Research Grant, Student Prize Committee, Survivors Party
  • Eric Swartz, Organising Committee, Faculty Research Grant, Daily Combinatorialist
  • Luke Morgan, Coffee machine maintenance, always-willing helper
  • Simon Smith, Pub Guide, daily pub organiser, always-willing helper
  • Gabriel Verret, Soccer organiser, always-willing helper
  • and of course, Cheryl Praeger, who allowed 70 or so survivors and friends to invade her house in 38C+ temperatures for the Survivors Party.



All the publications of our members that are deposited on the arXiv.

Published papers

  1. J. Bamberg, A. Betten, C. E. Praeger and A. Wassermann, Unitals in the Desarguesian projective plane of order 16,  J. Stat. Planning and Inference 144 (2014), 110-122.
  2.  J. Bamberg, M. Giudici, M. Liebeck, C. Praeger and J. Saxl, The classification of almost simple 3/2-transitive groups, Trans. Amer. Math. Soc. 365 (2013), 4257-4311.
  3.   D. Bubboloni, C. E. Praeger  and P. Spiga, Conjectures on the normal covering number of the finite symmetric and alternating groups,  International J. Group Theory 3 (2014), 57-75.
  4. J. Chen, C. H. Li and Á. Seress,  A family of half-transitive graphs, Electronic J. Combin.  20  (2013), 10 pp.
  5.   S. Dolfi, R. M. Guralnick, C. E. Praeger and P. Spiga, Coprime subdegrees for primitive permutation groups and completely reducible linear groups, Israel J. Math. 195 (2013), 745-772.
  6. W. Fan, D. Leemans, C. H. Li and J. Pan,  Locally 2-arc-transitive complete bipartite graphs, J. Combin. Theory Ser. A  120  (2013), 683-699. 
  7. N. Gillespie, D. Hawtin and C. E. Praeger, Elusive codes in Hamming graphs, Bull. Austral. Math. Soc. 88 (2013), 286-296.
  8. M. Giudici and C. Parker, There is no upper bound for the diameter of the commuting graph of a finite group, J. Combin. Theory Ser. A 120 (2013), 1600-1603.
  9.  M. Giudici and A. Pope, On bounding the diameter of the commuting graph of a group, J. Group Theory 17 (2014), 131-150.
  10. S.-T. Guo, Y.-Q. Feng and C. H. Li,  The finite edge-primitive pentavalent graphs, J. Algebraic Combin.  38  (2013), 491-497. 
  11. C. H. Li and S. Qiao, Finite groups of fourth-power free order, J. Group Theory  16  (2013), 275-298. 
  12. C. H. Li, S. J. Song and  D. J. Wang,  A family of edge-transitive Frobenius metacirculants of small valency, European J. Combin.  34  (2013), 512-521.
  13. C. H. Li, S. J. Song and D. J. Wang,  A characterization of metacirculants, J. Combin. Theory Ser. A  120  (2013), 39-48.
  14. C. H. Li, S. J. Song and H. Zhang,  Finite permutation groups with a regular dihedral subgroup, and edge-transitive dihedrants, J. Algebra  399  (2014), 948-959. 
  15. C. H. Li, S. Sun and J. Xu, Self-Complementary Circulants of Prime-Power Order, SIAM J. Discrete Math.  28  (2014), 8-17.
  16. C. H. Li and H. Zhang,  On finite 2-path-transitive graphs, J. Graph Theory  73  (2013), 225-237.  
  17. C. H. Li and H. Zhang,  Finite vertex-biprimitive edge-transitive tetravalent graphs, Discrete Math.  317  (2014), 33-43. 
  18. S. Noble and G. Royle, The Merino-Welsh Conjecture holds for series-parallel graphs, European J. Combin. 38 (2014), 24-35. 
  19. A.-G. Wu, W. Liu, C. H. Li and G.-R. Duan,  On j-conjugate product of quaternion polynomial matrices. Appl. Math. Comput.  219  (2013), 11223-11232. 

Accepted Papers

  1. M. Giudici, M. W. Liebeck, C. E. Praeger, J. Saxl and P. H. Tiep, Arithmetic results on orbits of linear groups, accepted in Trans. Amer. Math. Soc.
  2. W. Imrich, S. Smith, T. Tucker and M. Watkins, Infinite Motion and 2-Distinguishability of Graphs and Groups, accepted in J. Algebraic Combin.
  3. J. Kung, D. Mayhew, I. Pivotto and G. Royle, Maximum-sized binary matroids with no AG(3,2)-minor are graphic, accepted in Siam J. Discrete Math.
  4. P. Spiga and G. Verret, On intransitive graph-restrictive permutation groups, accepted in J. Algebraic Combin.
  5. E. Swartz, A construction of a partial difference set in the extraspecial groups of order p3 with exponent p2, accepted in Designs, Codes, and Cryptography.
  6. G. Verret, Arc-transitive graphs of valency 8 have a semiregular automorphism, accepted in Ars Math. Contemp.

Submitted papers

  1. B. P. Corr and C. E. Praeger, Normal Edge-Transitive Cayley Graphs of Frobenius Groups. arXiv:1401.1883.
  2. A. Devillers, W. Jin, C. H. Li and C. E.Praeger, Comparison of distance, geodesic and arc transitivity for finite graphs.
  3. N. Gillespie and C. E. Praeger, From neighbour transitive codes to frequency permutation arrays.   arXiv:1204.2900.
  4. M. Giudici and L. Morgan, A class of semiprimitive groups that are graph-restrictive. arXiv:1401.3086.
  5. M. Giudici, C. E. Praeger and P. Spiga, Finite primitive permutation groups and regular cycles of their element. arXiv:1311.3906.
  6. S. P. Glasby, C. E. Praeger and B. Xia, Decomposing modular tensor products, and periodicity of "Jordan partitions".  arXiv: 1401.2748.
  7. M. Iradmusa and C. E. Praeger, Two-sided Cayley graphs.  arXiv: 1401.2741.
  8. R. A. Liebler and C. E. Praeger, Neighbour-transitive codes in Johnson graphs. arXiv: 1311.0113.
  9. J. Morris, P. Spiga and G. Verret, Semiregular automorphisms of cubic vertex-transitive graphs. arXiv:1401.2940.
  10. J. Morris, P. Spiga and G. Verret, Automorphisms of Cayley graphs on generalised dicyclic groups.  arXiv:1310.0618.
  11. F. Pfender and G. Royle, Quartic graphs with every edge in a triangle. arXiv:1308.0081.
  12. P. Potočnik, P. Spiga and G. Verret, A census of 4-valent half-arc-transitive graphs and arc-transitive digraphs of valence two. arXiv:1310.6543.
  13. P. Spiga and G. Verret, On the order of vertex-stabilisers in vertex-transitive graphs with local group Cp × Cp or Cp wr Cp.  arXiv:1311.4308.


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