COMBINATORIAL MATHEMATICS SOCIETY OF AUSTRALASIA (INC)

CMSA E-Newsletter Number 2 (January 2000)

**INTRODUCTION**:

Happy New Year/Century/Millenium to all CMSA Members (since the media take 2000 rather than 2001 as the start of it all!). And thanks to the few members who have sent information for this newsletter: but we want MORE! Send in lists of visitors, news of members, conferences and workshops, births and deaths etc. It takes news from the members to make the newsletter!

CLOSING DATE for Issue 3: 31 May 2000.

Email ejb@maths.uq.edu.au with all your news and information.

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**Some WEB PAGES**:

CMSA: http://www.math.fsc.qut.edu.au/cmsa/

Centre for Discrete Mathematics and Computing, UQ: http://www.it.uq.edu.au/personal/havas/cdmc.html

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The AUSTRALASIAN JOURNAL OF COMBINATORICS reminds readers that billing is no longer through the University of Queensland, but is to the AJC direct. (The journal now accepts Visa, Mastercard and Bankcard.) Peter Adams is taking over from Colin Ramsey as Financial Manager of the AJC.

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AIMS of the newsletter:

- to promote combinatorics within Australasia
- to provide a forum for sharing combinatorial and related information
- to keep CMSA Members informed and in touch with combinatorial and related matters

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**RECENT CONFERENCE REPORTS**:

The Centre for Discrete Mathematics and Computing at the University of Queensland held a small Combinatorics Workship from 2 - 5 November 1999. One day was devoted to geometries, one to coding theory and cryptography, and two to design theory, graph decompositions and other combinatorics. Financial assistance from the Department of Mathematics is gratefully acknowledged.

On the Tuesday afternoon of 2nd November we had the obligatory pause for the famous Melbourne Cup horse race. A TV was provided in the lecture room for those interested; unspecified amounts of money were won and lost by workshop members.

On the Friday evening a survivors' party was held; despite several beers, one person managed to _cycle_ up the steep long driveway from the party venue, while another person ably walked home, despite having consumed an uncountable* number of Coopers (but not all the way to WA...).

* [according to the editor's teenage son, who's good at counting]

There were 18 talks presented:

- Peter Adams, UQ; Computational methods in combinatorics.
- Richard Bean, UQ; On the size of the largest critical set in a Latin square.
- Elizabeth Billington, UQ; Decompositions of complete tripartite graphs into gregarious 4-cycles.
- Matthew Brown, Adelaide; The Coney Island project: spreads of the GQ T2(O).
- Darryn Bryant, UQ; Very small embeddings of some partial triple systems.
- Linda Burnett, QUT; Evolutionary heuristics for finding cryptographically strong S-boxes.
- Bob Buttsworth, QUT; Edge and path operators on vertex functions.
- Gary Carter, QUT; An overview of methods for generation of elliptic curve cryptosystems.
- Ed Dawson, QUT; Methods for designing Boolean functions for cryptographic applications.
- Diane Donovan, UQ; Direct products and Latin interchanges.
- Rod Downey, Wellington; Parametric analysis of fundamental problems in coding theory.
- Nicholas Hamilton, UQ; Existence and non-existence of m-systems of polar spaces.
- Abdollah Khodkar, UQ; On minimal defining sets for the Steiner triple systems from affine geometry AG(d,3).
- Ebad Mahmoodian, Iran & UQ; Defining sets of graph colourings.
- Christine O'Keefe, Adelaide; On the magic action of PGammaL(2,q) and automorphisms of generalized quadrangles.
- Tim Penttila, UWA; Generalised quadrangles, translation planes and flocks of cones.
- Phil Pollett, UQ; On the evolution of some random graphs.
- Chris Rodger, Auburn; Some 4-cycle decompositions; removing trees/cycles etc.

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**FUTURE WORKSHOP AND CONFERENCE ANNOUNCEMENTS**:

**FINITE AND TOPOLOGICAL GEOMETRY WORKSHOP
**
Workshop on Finite and Topological Geometry and Related Topics hosted by the Institute for
Geometry and its Applications at the University of Adelaide, 17 - 21 January 2000.

For last minute details please contact the organisers, Christine O'Keefe or Burkard Polster, Department of Pure Mathematics, University of Adelaide, 5005;

Email cokeefe@maths.adelaide.edu.au or bpolster@maths.adelaide.edu.au

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**The 44th AUSTRALIAN MATHEMATICAL SOCIETY CONFERENCE
** will include a special session on combinatorics. This will be held at the
University of Queensland from 2 - 5 July 2000, starting about 11am on the SUNDAY. See the web
page http://AustMS2000.maths.uq.edu.au/

Contact Christine O'Keefe <cokeefe@maths.adelaide.edu.au> or Elizabeth Billington <ejb@maths.uq.edu.au> for further information on the combinatorics special session.

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**From 10-12 July 2000, QUT is hosting ACISP 2000,
**

Australasian Conference on Information Security and Privacy. This is the fifth
annual ACISP conference. Further information can be found at
http://www.isrc.qut.edu.au/acisp2K

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**The 25th ACCMCC will be held in Christchurch, New Zealand**,
from 4 - 8 December 2000.

For more details contact Charles Semple at
C.Semple@math.canterbury.ac.nz
or Mike Steel at
M.Steel@math.canterbury.ac.nz and see the web page
http://www.math.canterbury.ac.nz/accmcc.shtml

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**The next BRITISH COMBINATORIAL CONFERENCE, 18BCC**, will
be at the University of Sussex, Brighton, from 1 - 6 July 2001.
See web page available from
http://www.maths.sussex.ac.uk/TAGG/Confs/BCC/index.html

(Plan ahead for that overseas trip now! These are large conferences held each odd-numbered year in early July, although they are not as large as the Southeastern conferences in Boca Raton or Baton Rouge each March.)

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RECENT NEWS OF CMSA MEMBERS

NICHOLAS HAMILTON (currently at UQ on an ARC Fellowship) has been offered a two year postdoctoral fellowship at the University of Gent, Belgium, with Professor Frank De Clerck of the Department of Pure Mathematics and Computer Algebra. He will start sometime in May this year.

Frank De Clerck has been awarded a grant worth about $2,000,000, for work on structures in finite projective spaces. Other members at Gent include Jef Thas, Hendrik Van Maldeghem and Leo Storme.

MATTHEW BROWN took up a similar fellowship in December last year.

[Ed's note: I asked Nicholas for any news, gossip etc., for this newsletter, and he also
said:
*P.S. Can't think of any gossip that is fit to print. Most of the interesting things I know
would result in court actions. *]

Those of you who remember REBECCA GOWER (PhD UQ) might be interested to hear that she is now working for a company called Numbercraft in Oxford, UK, at the Oxford Science Park.

PETER ADAMS has been offered a tenurable lectureship at UQ.

NICK WORMALD has a nice review in the recent (December 1999) Australian Mathematical Society's Gazette, for those of you who are members of the AustMS, of the book by Fan Chung and Ron Graham, `ERDOS ON GRAPHS: his legacy and open problems'.

(The same issue of the AustMS Gazette has some nice photos taken at the 2-day function held in honour of BERNHARD NEUMANN'S 90th birthday at ANU on October 15 and 16 1999.)

CURT LINDNER'S position as Honorary Professor in the Department of Mathematics at UQ has been renewed to the end of 2002. (Curt is of course still in the Department of Discrete and Statistical Sciences at Auburn University.)

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VISITORS

DEAN HOFFMAN from Auburn will visit UQ, 8 March - 29 March 2000.

EBAD MAHMOODIAN is at UQ, on leave from Sharif University in Iran, until October 2000.

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MEMBERS' RECENT RESEARCH DEGREES

Congratulations to IAN ROBERTS and PAULETTE LIEBY on their recent doctorates. Ian's thesis is "Extremal problems and designs on finite sets", and Paulette's is "Extremal problems in finite sets".

Congratulations also to OUDONE PHANALASY on his Masters, with thesis entitled "Covering separating systems".

Congratulations also go to BARBARA MAENHAUT and MARKS NESTER, who received their PhDs from UQ in March and October 1999. Barbara's thesis was entitled "Substructures of cycle systems with applications to access schemes"; she now has a lectureship at the Open University in Britain. Marks' thesis was entitled "Mathematical investigations of some plant interaction designs".

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**PREPRINTS/RECENT PUBLICATIONS BY MEMBERS**:

GRAHAM NORTON, Bristol UK, has sent in the following:

T. Blackmore and G.H. Norton,

On the state complexity of some long codes,

Finite Fields, Theory, Applications and Algorithms.

Contemporary Mathematics vol 225, 203-214, Amer. Math. Soc. (1998).

T. Blackmore and G.H. Norton,

On the trellis structure of GRM codes,

Algebraic and Combinatorial Coding Theory VI (1998), Pskov, 26-29.

G.H. Norton,

On shortest linear recurrences,

J. Symbolic Computation 27 (1999), 325-349.

G.H. Norton,

On minimal realization over a finite chain ring,

Designs, Codes and Cryptography 16 (1999), 161--178.

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No one else has sent in details, so let me add my bit!

Here's one fast off the rank; can anyone beat this timewise?

(Perhaps I should thank the referee in case s/he is reading this!!)

Elizabeth J. Billington and C.C. Lindner,

The metamorphosis of lambda-fold 4-wheel systems into lambda-fold
4-cycle systems, Utilitas Mathematica (to appear).

Work was begun on this in mid/late August 1999; the paper was submitted to Utilitas
Mathematica on 12 October 1999 and accepted 12 November 1999.

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REMINDER: deadline for next issue 31 May 2000.

Elizabeth Billington, Dept Maths, UQ, Qld 4072.

ejb@maths.uq.edu.au

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