Interim Report for 2009 and 2010

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Nov 21, 2013 (4 years and 1 month ago)

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CENTRE FOR DISCRETE MATHEMATICS AND COMPUTING

in the

DISCIPLINE of MATHEMATICS,
SCHOOL of MATHEMATICS and PHYSICS

and the

SCHOOL of INFORMATION TECHNOLOGY and ELECTRICAL ENGINEERING

at

THE UNIVERSITY OF QUEENSLAND


Interim
Report for 20
09 and 2010

April 20
11


Preface


In 20
09 and 2010

the Centre was located in the School of
Mathematics and Physics
.
It was formed
at the beginning of 1998 by the merger of the Centre for Combinatorics (in the then Department of
Mathematics) with the Algorithms Group (in the th
en Department of Computer Science and
Electrical Engineering). The Centre promotes research in combinatorics and in algorithm design,
and supports the Number Theory Web. It acts as
a
national base for an international body, the
Institute of Combinatoric
s and its Applications (ICA), and as
a
regional base for the Combinatorial
Mathematics Society of Australasia (Incorporated) (CMSA (Inc)).
The international journal,
The
Australasian Journal of Combinatorics
, is published by the Centre, for the Combinatori
al
Mathematics Society of Australasia Inc. The journal has an international Editorial Board, while its
Managing Editors are all from Australia or New Zealand. The Centre
is one of twenty
-
one groups
listed on the World Combinatorics Exchange

http://www.combinatorics.org/People/index.html#groups
. The Centre periodically hosts conferences
and workshops,
with a workshop being planned for September 2011
.


Members of the Centre actively collabor
ate with overseas research groups in Canada, China, Czech
Republic, Finland, Germany, Iran, New Zealand, Taiwan, Thailand, Turkey, United Kingdom and
United States of America. Within Australia, members of the Centre collaborate with research
groups at: th
e Universities of Monash
;

Newcastle
;

New South Wales
;

Southern Queensland
;

the
University of Technology, Sydney
;

and the Queensland University of Technology. The Centre also

hosts numerous visitors, including a num
ber of Ethel Raybould Research F
ellows.
Postgraduate
students within the Centre have the benefit of working with such visitors while they are here, and
sometimes of visiting them in their home universities.


Members of the Centre have easy access to the Dorothy Hill Engineering

and Sciences

Libr
ary of
The University of Queensland, which houses one of the best collections in Australasia of
combinatorial literature. They also have access to computing facilities appropriate to their needs.


Although both discrete mathematics and computing are areas

of much serious research, they include
many problems which are easily stated and understood, and consequently of interest to people with
little formal background in the area. Some of these problems are immensely difficult, the four
colour theorem and Fer
mat's last theorem being classic examples. Some are relatively easy to solve,
at least in small particular cases, and attract students into the area, and often from there into other
areas of mathematics as well. Thus many combinatorial questions feature
on the Queensland
Association of Mathematics Teachers Problem Solving Competitions, the Australian Mathematics
Competitions, and the Mathematical Olympiads. Areas where such questions arise include games
and puzzles, scheduling and allocation problems, co
ding and cryptography, structures of woven
textiles, and many problems in graph theory. Staff associated with this Centre have contributed
consistently to activities for secondary students, including competitions,
Experience Science week
,
School visits, a
biennial newsletter (Infinity) and the club allied with it (Club Infinity).


Theoretical interests within the Centre include: designs, networks and graphs; universal algebras
and their relation to designs and graphs; number theory; finite fields; combinato
rial computing,
especially algorithm development relevant to these areas, to linear algebra and to parallel and
distributed computing. Applications of particular interest inclu
de: experimental design; error
-
correcting codes and cryptography; techniques fo
r drug design, combinatorial chemistry and DNA
sequencing; and the production of scientific software now included in such large systems as
MAGMA (based at the University of Sydney), GAP (Scotland), LIDIA and KANT (Germany) and
PARI (France).


1. STAFF A
SSOCIATED WITH THE CENTRE


Centre Director
:

Associate
Professor

Diane Margaret Donovan, BA, DipEd
La Trobe,

PhD, FTICA, FAustMS
(combinatorial designs
and computer security schemes)


Professor
s

Peter Adams, BSc (Hons), BComm, PhD, FTICA
(combinatorial de
signs, combinatorial computing
and applications)


Darryn Edward Bryant, BSc, MScSt, PhD, FTICA
(combinatorial designs, graph theory and DNA
sequencing)


Ole Warnaar,
PhD
Amsterdam
, FAA
,
(Algebraic combinatorics
, q
-
series and partition theory
)


Honorary Pro
fessor
s

Anne Penfold Street, MSc
Melb
, PhD
Ill,

DMath
UW
, FTICA
(combinatorial designs and
applications)


Charles Curtis Lindner BS
Pres, Clinton, S.C,

MS, PhD
Emory
, FTICA
(combinatorial designs)
1


George Havas, BA Hons
ANU
, PhD

Sydney

(algorithm des
ign)


QEII Fellows


Benjamin Burton, BSc Hons
UQ,
PhD,
UMelb,
(geometry and topology, with a focus on spaces in
three and four dimensions)


Associate Professors

Elizabeth Jane Billington, MA, DipAdMaths
Oxon
, DipEd, PhD, FTICA, FAustMS

(combinatorial
desi
gns and graph decompositions)


Lecturers

Barbara Marguerite Maenhaut, BMath
UW
, BE
d

UWO
, PhD, FTICA
(combinatorial designs,
graph theory)


Stephan Tillmann, BSc Hons,
UMelb,
PhD,
UMelb,(Geometry and Topology)


Victor Scharaschkin, BSc Hons
Tas
. PhD

Mi
ch


(algebraic number theory, arithmetic geometry)


Associate
Lecturer

Mary Waterhouse, BSc Hons, PhD,
(combinatorial designs, graph theory)





1

Distinguished Professor, Auburn University

Senior Research Officers

Kenneth Raward Gray
2

BA (Hons), DipEd
Macquari
e, PhD, FTICA
(combinatorial designs and
education)


Research Officer
s

James Lefevre, BSc Hons Tas. PhD,
(combinatorial designs, graph theory)


Matthew Dean, Matthew,
BSc Hons PhD

(combinatorial designs, graph theory)


Honorary Research Consultants

Keith Robert Matthews, MSc, PhD

(number theory)


Graham Hilton Norton, BSc
Cape Town
, PhD
Cornell

(applied algebra, algebraic coding theory,
number theory)



2. RESEARCH STUDENTS

Awarded 20
09
-
2010


Thomas McCourt
, (PhD,
On Defining Sets in Latin Squares and two Intersection Problems, one for
Latin Squa
res and one for Steiner Triple Systems
,

Donovan
/
Lefevre
)


Benjamin R. Smith (PhD,
Decompositions of generalised complete graphs
,
Billington/Jones/Cavenagh)


Judith Egan,
(PhD
Monash University,
Generalised Transversals of Latin Squares

(
Bryant/Wanless,
Mon
ash U)


Current Research Students


Nicholas Bartlett, (PhD,
Rogers
-
Ramanujan identities on root systems
,
Warnaar
)


Nicholas Coxon, (P
h
D,
On Polynomial Selection for the Number Field Sieve
,
Scharaschkin/Carter)


Fatih Demirkale
, (P
h
D
,
Defining sets and asso
ciated trade structures for combinatorial
configurations
, Donovan/Burton)


Nazer Halimi, (P
h
D,
Ideal theory of cones and Dubrovin valuation rings,

Warnaar/Elder)


Sam
uel
Hambleton, (P
h
D,
Primality testing in number theory
,
Scharaschkin/Carter)


Sarada Herk
e, (PhD,
Factorisations of graphs

, Maenhaut/Bryant)


Geoff
rey
Martin,
(PhD,

Cycle decompositions of circulant graphs
,
Bryant/
Maenhaut
, submitted
)





2

Senior Research Officer (p/t); Consultant in educational assessment and testing, with clients including both Education
Queensland and non
-
state schools

Trevor Pickett, (P
h
D,
An
investigation of combinatorial configurations and their substructures,

Donovan/Adam
s)


Current
Honours

Students


Carly Bodkin, (Honours, Optical Orthogonal Codes, Maenhaut)


John Flemming, (Honours, The Oberwolfach Problem, Maenhaut)


Jenna Thompson, (Honours, Authentication Schemes from Combinatorial Designs, Maenhaut)


3. VISITORS

Dr M
atthew Dean (Qld Academy for Creative Industries) Jan 2010


Dec 2010

Dr Melih Ozlen (RMIT) 30 Mar 2010
-

10 Apr 2010

Prof Terrence Griggs (The Open University) 13 Apr 2010
-

06 May 2010

Dr Ryan Budney (Univer
si
y of Victoria, Canada) 20 Jun 2010
-

23 Jul

2010

Prof Alain Lascoux (IGM Universite de Marne
-
La
-
Vallee, France) 10 Jun 2010
-

20 Jul 2010

A/Prof Abdollah Khodkar (University of West Georgia, USA) 02 Sep 2010
-

30 Sep 2010

Dr
Melih Ozlen (RMIT) 26 Aug 2010
-

02 Sep 2010

Dr Melih Ozlen (RMIT) 15 N
ov 2010
-

19 Nov 2010

Dr Henry Segerman (Univ of Melbourne) 26 Oct 2010
-

15 Nov 2010

Dr Nicholas Cavenagh (University of Waikato,
NZ
) 07 Jan 2009
-

17 Jan 2009

Prof Mike Grannell (
Open University, UK) 04 Feb 2009
-

13 Feb 2009

Prof Deborah Street (Uni
versity of Technology, Sydney) 29 Jan 2009
-

11 Feb 2009

Prof Vyacheslav Spiridonov (Joint Institute for Nucl
ear Research, Russia) 15 Feb

-

06 Mar 2009

Prof Terence Griggs (The Open University, London) 07 Mar 2009
-

01 Apr 2009

Dr Nicholas Cavenagh (Uni
versity of Waikato,
NZ
) 06 Apr 2009
-

20 Apr 2009

Dr Ian Wanless (Monash University) 23 Apr 2009
-

03 May 2009

Dr Vyacheslav Abramov (Monash University) 21 May 2009
-

22 May 2009

Dr Bridget Webb (The Open University, England) 25 May 2009
-

05 Jun 2009

P
rof Curt Lindner (Auburn University) 13 Jul 2009
-

25 Jul 2009

Prof Roger Eggleton (Illi
nois State University) 03 Aug 2009
-

07 Aug 2009

Dr Nick Cavenagh (University of Waikato, NZ) 19 Oct 2009
-

23 Oct 2009

Dr Nick Cavenagh (Waikato University
, NZ
) 14
Dec 2009
-

24 Dec 2009


4. RESEARCH INTEREST
S


Combinatorial Designs and Graph Theory


Designs as graph deco
mpositions. Trades in graphs.
Graph decompositions and colourings.

Gregarious systems.

Metamorphosis of designs, including
G
-
designs.

Bipartite a
nd tripartite
designs; cycle system
s, Hamilton/Waterloo problems.
Triple systems, espe
cially Steiner triple
systems.
Inte
rsection problems for designs.
Blocking sets in designs.
Partitioning families of blocks
into collections of disjoint de
signs, includin
g small planes.
Defining sets of designs and critical sets
of Latin squares; trades and Latin interchanges. Defining sets and trades in other combinatorial
structures.

Proportionally balanced designs, constructions and properties.


Applications of discret
e mathematics

DNA sequencing, Encoding/decoding methods for combinatorial chemistry, optimization of
combinatorial chemistry techniques. Drug design. Bioinformatics. Application of combinatorial
designs to authentication schemes, to the construction of a
ccess schemes for computer security and
to the
construction of block ciphers.
Classes of designs for the study of plant competition, of
scheduling and allocation problems, and of problems in cognitive science.

Application of
proportionally balanced designs

to allocation of marking, comparison of syllabi and checking
suitability of questions for Core Skills Tests.


Combinatorial Designs: relationships with universal algebras

Relationships between quasigroups and certain types of neighbourhood designs; when t
he
p
articular
quasigroups involved actually form a variety. The study of distances of between Latin squares and
associated geometric surfaces. Universal algebra techniques applied to construct new designs.
Small 2
-
perfect designs. Strongly 2
-
perfect cyc
le systems and associated quasigroups.


Algebra and Number Theory

Ramsey varieties of finite groups, the topological group of
p
-
adic integers, varieties of congruence
lattices of groups. Homological algebra and ring theory. Cohomology rings of finite gro
ups.
Group representation theory. Formal methods for computing, symbolic computation. Homotopy
theory. The Brauer Manin obstruction. The ABC conjecture. Arithmetic geometry. Rational
points on varieties.


Combinatorial

Computing and Algorithm Design

Abstract algebraic algorithms. Perfect hashing. Fundamental algorithms for parallel and distributed
systems. Finite fields and their applications. Computational combinatorics. Algorithm
d
evelopment for linear algebra. Computing canonical forms of matr
ices. Extended GCD
algorithms.


Algebraic combinatorics


Geometric group theory
,
combinatorics
,
generic complexity

of combinatorial and group theoretic
problems, automata and language theory
.
Macdonald polynomials, Hall
-
Littlewood functions,
Kostka
-
Foulkes polynomials.


Basic and elliptic hy
pergeometric series
-

beta integrals, series based
on root systems
,

q
-
Series and partition theory
-

Rogers
-
Ramanujan identities, Bailey's lemma, the
Borwein conjecture.

Representation theory
-

characters of infinite
-
dimensional Lie algebras.

Special functi
ons
-

elliptic functions, orthogonal polynomials, Selberg integrals.


6. RESEARCH FUNDING


Bryant

Cycle decompositions of graphs,

$435,000, ARC 2007
-
2011



With Wanless,
Analysis of the structure of Latin squares
, $350,000, ARC, 2006
-
2010.


Burton

Algorit
hms and computati
on in four
-
dimensional topology
.

$625,000,
ARC

DP with QEII
Fellowship

2010

2014


Fast algorithms for string processing in cryp
tography and bioinformatics
, $11936,

UQ, 2010


Burton and Tillmann,

With
M.

Elder,
Generic complexity in compu
tational topology: Breaking through the bottlenecks,

$255,000,
ARC,

2011

2013


Donovan

With DJ Street,
A systematic investigation of how to design stated choice experiments that

provide the best predictive outcome for policy makers,
$155,000, ARC, 2010
-
20
12


With
Wood, Joshi, Loch, Donovan, Bloom, Bower, Brown, Skalicky,
A national discipline
-
specific
professional development program for lecturers and tutors in the mathematical sciences
,
$236,000,
ALTC,
2009
-
2010


Donovan and Lefevre

Research Teaching Fel
lowship, $4
0000, University of Queensland, 200
9
-
10

Maenhaut

Factorisations of graphs, $35,000, University of Queensland, 2008
-
10.


Tillman

With
Hodgson and Rubinstein,
Triangulations in dimension three: algorithms and geometric
structures
,

ARC
,

2010
-
2012


Ch
aract
er varieties of 3
-
manifold,

UQ, 2009


7. INVITATIONS

AND
PRESENTATIONS


Billington

Invited
plenary
speaker:
Some interesting graph decompositions
,
Canadian Mathematical Society
Meeting, St Johns, Newfoundland, Canada, June 2009.

Conference talk:
Al
most resolvable

4
-
cycle systems: maximum packings
, 33 ACCMCC, University
of Newcastle, December 2009.

Seminar Speaker:
Gregarious cycles: an antipodean update
, Auburn University, USA, July 2010.

Seminar Speaker:
Some interesting graph decompositions
, Aubur
n University,

USA,

August 2010.

Conference talk:

An extra condition on twofold

2
-
perfect cycle systems
, 54
th

Australian
Mathematical Society meeting, September 2010.
Seminar Speaker:
Gregarious multipartite
graph decompositions
, University of Waikato, Hamil
ton, New Zealand, October 2010.


Burton

Conference talk:
Is simplifying triangulations as hard as it seems?

ACCMCC, ANU
, December
2010

Seminar Speaker:
The Pachner graph and the simplification of 3
-
sphere triangulations
, Melbourne
University, November 2010

Seminar Speaker:
Linear programming, combinatorial geometry and the perfect sausage

, RMIT,
November 2010

Conference talk:
Is simplifying triangulations as hard as it seems?

AustMS Annual Meeting,
UQ
,
September 2010

Seminar Speaker:
Encouraging algorithmi
c thinking without a computer
, IOI, Canada, August
2010

Workshop Speaker:
Polytopes, combinatorics and complexity in computational topology

Combinatorics and Mathematical Physics 2010, Brisbane, July 2010

Workshop Speaker:
Computational topology in four
dimensions

Algorithms, Algebra and Analysis
in Four Dimensions, Brisbane, July 2010

Workshop Speaker:
Computer session
Algorithms, Algebra and Analysis in Four Dimensions,
Brisbane, joint with Ryan Budney, July 2010

Conference Speaker:
Problem setting
in mathematics and informatics Weaving proof into
programming

WFNMC Congress, Latvia, July 2010

Workshop Speaker:
Communication and cooperation A report on the 2010 Informatics Olympiad
workshop

WFNMC Congress, Lavtia, July 2010

Seminar Speaker:
The
complexity of the normal surface solution space

SCG, Snowbird, USA, June
2010

Seminar Speaker:
Linear programming, combinatorial geometry and the perfect sausage
,

UQ,
May 2010

Seminar Speaker:
Polytopes, combinatorics and complexity in computational to
pology
,
Oxford
University, UK, May 2010

Workshop Speaker:
Developing an international repository of problems

IOI Wo
rkshop, Germany,
May 2010

Workshop Speaker:
Using a wiki for peer
-
to
-
peer teaching and learning

IOI Workshop, Germany,
May 2010

Confere
nce Speaker
:
Fast, faster, fastest Algorithms in cryptography and bioinformatics
,

Gro
up
Theory International Webinar, April 2010

Seminar Speaker:
A short history of 3
-
sphere recognition
,
UQ, March 2010

Workshop Speaker:
The Weber
-
Seifert doDecemberahed
ral space Answering a computational
challenge
,
Mini
-
workshop Topolo
gy of the Space of Knots, Japan, February 2010

Seminar Speaker:
Normal surfaces Taming the wild algorithms of topology
,
Nih
on University,
Japan, February 2010

Seminar Speaker:
The feasi
bility of algorithms in 3
-
manifold topology
,
Melbourne University,
December 2009

Seminar Speaker:
Algorithms and computation in three
-
dimensional topology
,

ANU, December
2009

Seminar Speaker:
The feasibility of algorithms in 3
-
manifold topology
,
UQ, De
cember 2009

Seminar Speaker:
Fast, faster, fastest Algorithms in cryptography and bioinformatics
,

RMIT,
November 2009

Seminar Speaker:
The Weber
-
Seifert doDecemberahedral space Theory, algorithms and
computation in 3
-
manifold topology
,
Melbourne Univer
sity, November 2009

Seminar Speaker:
Fast, faster, fastest Algorithms in cryptography and bioinformatics
,

UQ, October
2009

Seminar Speaker:
An introduction to computational topology
,

UQ, May 2009




Donovan

Invited Conference Speaker:
Latin squares,
Latin trades and related problems,

2nd Mile High
Conference on Nonassociative Mathematics, University of Denver, June 2009.

Contributed talk:
Latin square and Determinants
,
The 34th Australasian Conference on
Combinatorial Mathematics and Combinatorial Com
puting (34ACCMCC), Canberra, December
2010

Contributed talk:
“10 Years Ahead”,

joint with Birgit Loch,
2010 Australasian Tablets in Education
Conference, Melbourne, December 2010

Seminar Speaker:
Latin square and Determinants,

RMIT, November 2010

Seminar S
peaker:
Latin squares, latin trades and related problems,
UQ, May 2009

Seminar Speaker:
Latin trades and the completion of partial latin squares,

RMIT, August 2009

Seminar Speaker:
Determinants of Latin Squares,

at Monash University, August 2009

Seminar S
peaker:
Change Detection via Spectral Analysis in Dynamic Enterprise Networks
, Kings
College London, October 2009

Seminar Speaker:
The importance of latin trades in the study of completing partial latin squares
,
Queen Mary College, October 2009

Seminar Sp
eaker:
Results on latin trades and defining sets for Latin squares
, Koc University
Istanbul, November 2009


Gray

Contributed talk: A method for constructing defining sets of all (v,k,λ) designs

Fifth Asian Mathematical Conference, June 22


26, 2009, Kuala Lumpur, Malaysia.



Maenhaut

Invited Conference Speaker: 24th Mid
-
western Conference on Combinatorics, Cryptogra
phy and
Computing, Illinois State University, USA, September 2010.

Invited Conference Speaker: 34th Australasian Conference on Combinatorial Mathematics and
Combinatorial Computing, University of Newcastle, Australia, December 2009.


8. SEMINARS

PRESENTED

WITH
IN

THE CENTRE

2010

Murray Elder, Maths UQ,
Computing geodesics in BS(1,p) in linear time
,
Jan 19

Stephan Tillmann, Maths UQ,
Spinning, straightening and the recognition of closed hyperbolic 3
-
manifolds,

Feb 2

Ole Warnaar, Maths UQ,
Happily ever after .
...

Mar 16

Murray Elder, Maths UQ,
Generating functions and context
-
free grammars
,

Mar 23

Melih Ozlen, RMIT,
Nonlinear multi
-
objective integer programming: A general approach for
optimization,

Mar 30

Joel Hass, UC Davis,
Complexity of Unknotting,

April 20

Darryn Bryant, Maths UQ,
An introduction to graph decompositions
,

May 11

Ben Burton, Maths UQ,
Linear programming, combinatorial geometry and the perfect sausage,

June

1

William Pettersson, Maths UQ,
The Post Correspondance Problem
,

June

8

Ryan Budney, Uni
versity of Victoria, BC, Canada,
Knots so far
, July 6

Andrew Rechnitzer, UBC, Canada
,
GAS sampling of polygons and knot probability ratios
,

July 15

Stephan Tillmann, Maths UQ
,
Volume of representations
,

Aug 3

Tim Trudgian, University of Lethbridge, Canada
,
On the zeroes of the Riemann zeta
-
function
,

Sept
7

Abdollah Khodkar, University of West Georgia, USA
,
Super edge
-
graceful labelings of complete
bipartite graphs
,

Sept 14

Alexander Hulpke, Colorado State University, USA
,

Computing Conjugacy Classes in Mat
rix
Groups
,

Oct 19

Henry Segerman, University of Melbourne
,
A generalisation of the deformation variety
,

Oct 26


2009

Peter Neumann
,

Oxford University, UK
,

The
Memoirs of Évariste Galois
,

Jan 22

Mike Grannell
,

Open University, UK
,

Rigid Steiner 5
-
designs
,

Feb 10


Andrew Rechnitzer


University of British Columbia,
Canada
,
A
pproximate counting and
atmospheres
,


Feb 17


Slava Spiridonov
,

Joint Institute for Nuclear Research,

Dubna, Russia
,

Elliptic
hypergeometric
functions
,

Feb 24


Terry Griggs
,

Open University, UK
,

The design of the century
,

Ma
r 16


Murray Elder
,
Maths, UQ
,

Geodesics in the Grigorchuk group
,

Mar 31

George Havas
,

ITEE, UQ
,

On counterexamples to the Hughes conjecture
,

Apr 7


Ian Wanless
,

Monash University
,
The nearest group
,

Apr 28


Ben Burton
,

RMIT
,

An introdu
ction to computational topology,

May 7




Nick Coxon
,

Maths, UQ
,

The LLL algorithm
,

May 19

Bridget Webb
,

Open University,

Countably infinite Steiner triple systems
,

May 26



Diane Donovan
,

Maths, UQ
,

Latin squares, Latin trades and related problems
,

Jun 9


Nick Davis
,

University of Melbourne,

Self
-
similar groups and dynamics
,

Jun 30


Adam Piggott
,

Bucknell University, USA
,

Normal forms for automorphisms of groups
,

Jul 7


Daniel Horsley
,

Memorial University of Newfoundland,

Canada
,
Weak colourings of cycle
systems
,

Jul 8

Bernard Nienhuis
,

University of Amsterdam
,

Critical percolation and qKZ equations
,

Jul 13

Curt Lindner
,

Auburn University, USA,

Can grid systems be equationally defined?


Jul 15


Curt Lindner
,

Auburn Unive
rsity, USA
,

Almost resolvable 4
-
cycle systems
,

Jul 20


Edward Saff
,

Vanderbilt University
,


Discrete Minimal Energy Problems
,

Jul 27


Jose Burillo
,

Universitat Politècnica
de Catalunya,

Barcelona, Spain,

The Banach
-
Tarski paradox
,

Aug 3

Stephan Tillmann
,

Maths, UQ
,

Bounds for the complexity of 3
-
manifolds
,

Aug 11


Stephan Tillmann
,

Maths, UQ
,

Bounds for the complex
ity of 3
-
manifolds #2
,

Aug 18


Nick Coxon
,

Maths, UQ
,

Hilbert's tenth problem
,

Aug 25

Graham Norton
,

Maths, UQ
,

A fibrewise free
-
abelian
-
group functor
,

Sept 1



Graham Norton
,

Maths, UQ
,

Schemes from Scratch: Finite Set
s
,

Sept 25

Pee Choon Toh
,

Maths, UQ
,

The partition function, congruences and Dedekind’s eta function
,

Sept
22

Ben Burton
,

Maths, UQ
,


Fast, faster, fastest: Algorithms in cryptography and bioinformatics
,

Oct 6
David Baraglia
,

Oxford University,

G2 manifolds and coassociative fibrations
,


Oct 20


Ben

Burton
,
Maths, UQ
,


The feasibility of algorithms in 3
-
manifold topology
,

Nov 24


9
.
EDITORIAL WORK


The Centre publishes the
Australasian Journal of Combinatorics,

an internati
onal journal, for the
Combinatorial Mathematics Society of Australasia (Incorporated). Billington is Editor
-
in
-
Chief,

Professor Gordon Royle (University of Western Australia) is Chief Managing/Production Editor,
and Adams is Financial Manager. Other Mana
ging Editors are Dr Nicholas Cavenagh (Waikato,
New Zealand); Dr Diana Combe (UNSW); Dr Catherine Greenhill (UNSW); Professor Charles
Little (Massey, New Zealand); Maenhaut (UQ); Dr Kevin McAvaney (Deakin) . Associate Editors
include Adams, Bryant, Donovan

and Havas. Of the 20 members of the Editorial Board,
eight
work
within Australia and New Zealand
, and the remaining
13

form an
i
nternational network of
combinatorialists in Canada, Germany, Greece,
the
United Kingdom and
the
United States of
America.



Ma
tthews maintains a World Wide Web site called The Number Theory Web,
http://www.numbertheory.org/ntw/
. The site provides links to nearly 500 number theorists' home
pages throughout the world, centres, book descriptions, surveys, recent theses, conference
i
nformation and libraries with good holdings in the number theory field.


CMAT and CALC are exact arithmetic matrix and number theory packages developed by Matthews
for use mainly in teaching. For more information see the WWW address
http:/
/www.maths.uq.ed
u.au/~krm/


The following staff associated with the Centre have served in other editorial capacities during
2009
-
10
.


Billington is

a member of the Editorial Boards of
Utilitas Mathematica

and
Journal of
Combinatorial Mathematics and Combinatorial Computin
g.

She reviews for
Mathematical
Reviews

and referees for
journals including:
Journal of Combinatorial Designs, Ars
Combinatoria, Discrete Mathematics, Bulletin of the Institute of Combinatorics and its
Appli
cations,

Linear Algebra and its Applications,

Jou
rnal of Graph Theory

and
Journal of
Algebraic Combinatorics.


Bryant is a member of the editorial board of the
Journal of Combinatorial Designs
. He reviews for
Mathematical Reviews

and referees for
Ars Combinatoria, Bioinformatics, Bulletin of the
Australi
an Mathematical Society, Bulletin of the Canadian Mathematical Society, Discrete
Mathematics, Graphs and Combinatorics, Journal of Combinatorial Designs, Journal of
Combinatorial Mathematics and Combinatorial Computing, Journal of Combinatorial Theory
seri
es A, Journal of Combinatorial Theory series B, Journal of Graph Theory and Utilitas
Mathematica
.


Donovan is a member of the Editorial Board of
Ars Combinatoria
. She referees for the
Bulletin

and
the
Gazette

of the
Australian Mathematical Society,

and fo
r
Annals of Combinatorics,

Austral
as
ian Journal
o
f Combinatorics
,

Discrete Mathematics
,
European Journal of
Combinatorics, Journal of Combinatorial Mathematics and Combinatorial

Computing
,
Applicable Analysis and Discrete Mathematics

and

Utilitas Mathemati
ca
.



Maenhaut reviews for
Mathematical Reviews

and referees for
Australasian Journal of
Combinatorics
,
Bulletin of the Institute of Combinatorics and its Applications,

Discrete
Mathematics
,
Electr
onic Journal of Combinatorics,
Graphs and Combinatorics,
I
nformation
Processing Letters
,

Journal of Combinatorial Designs,

Journal of Combinatorial Theory Series
A,

Journal of Combinatorial Mathematics and Combinatorial Computing,
and

Utilitas
Mathematica.


Street is a member of the editorial boards o
f Ars Combi
natoria, Ars Textrina, Bulletin of the
Institute of Combinatorics
and

its Applications
and

Scientia Iranica.
She also referees for
Discrete

Mathematics,
Journal of Combinatorial Mathematics and Combinatorial C
omputing
and

Utilitas Mathematica.


10. COLLA
BORATIONS

Billington

Professor Catharine Baker; Mount Allison University, Sackville, Canada

Dr Nicholas J Cavenagh; Monash University

and University of Waikato, NZ

Professor Hung
-
Lin Fu; National Chiao
-
Tung University, Hsin
-
Chu, Taiwan

Professor D G Hoffm
an; Department of Mathematics and Statistics, Auburn University, USA

Professor A. Khodkar; Department of Mathematics, University of West Georgia, USA

Professor Selda Kucukcifci; Department of Mathematics, Koc University, Istanbul, Turkey

Professor C C Lind
ner; Department of Mathematics and Statistics, Auburn University, USA

Professor Mariusz Meszka, Faculty of Applied Mathematics, AGH University of Science and
Technology, Krakow, Poland

Professor C A Rodger; Department of Mathematics and Statistics, Auburn
University, USA

Professor Alex Rosa; Department of Mathematics and Statistics, McMaster University, Canada

Professor W D Wallis;
Department of Mathematics,
Southern Illinois University at Carbondale,
USA

Professor Emine Sule Yazici; Department of Mathemati
cs, Koc University, Istanbul, Turkey


Bryant

Professor P. Danziger; Department of Mathematics, Ryerson University, Canada.

Professor S. I. El
-
Zanati; Mathematics Department, Illinois State University, U.S.A.


Professor S. G. Hartke; Department of Mat
hematics, University of Nebraska, U.S.A.

Dr D. J. Horsley; Department of Mathematics and Statistics, Memorial University of
Newfoundland, Canada.

Professor P. R. J. Östergård; Department of Communications and Networking, Helsinki
University of Tech
nology, Finland.

Professor C. A. Rodger; Department of Discrete and Statistical Sciences, Auburn University,
U.S.A.

Dr I. M. Wanless; School of Mathematical Sciences Monash University, Australia.


Donovan

Dr Nicholas Cavenagh;
Monash University and Uni
versity of Waikato, NZ

Professor Ales Drapal; Charles University, Czech Republic

Professor Mike Grannell; Open University, UK

Professor Terry Griggs; Open University, UK

Dr Carlo Hamalainen; Charles University, Czech Republic

Dr Michael Hoffman; Universit
y of Leicester, UK

Prof Abdollah Khodkar; University of West Georgia, USA

Professor Charles Lindner; Auburn University USA

Dr Birgit Loch; University of Southern Queensland

Professor E S Mahmoodian;

Sharif University of Technology, Tehran, Iran

Prof. Deb
orah Street; Uni of Technology, Sydney

Prof Sule Yazici; Koc University, Turkey


Havas

Professor G Baumslag; City University of New York, USA

Dr C M Campbell; St Andrews University, UK

Professor M D E Conder; University of Auckland, NZ

Professor G C
ooperman; Northeastern University, USA

Professor D F Holt; University of Warwick, UK

Professor S A Linton; St Andrews University, UK

Professor C F Miller;

The University of Melbourne

Professor M F Newman; Australian National University

Professor E A
O'Brien;
University of Auckland, NZ

Professor E F Robertson; St Andrews University, USA

Professor C C Sims; Rutgers University, USA

Dr D C Sutherland;
St Andrews University, UK

Professor D Troeger; City University of New York, USA

Professor M R Vaug
han
-
Lee; Oxford University, UK

Professor E S Yazici; Koc University, Turkey


Lefevre

Dr Atif A. Abueida; University of Dayton, USA

Dr Nicholas Cavenagh;

University of New South Wales

Professor Ales Drapal; Charles University, Czech Republic

Professor M
ike Grannell; Open University, UK

Professor Terry Griggs; Open University, UK

Dr Carlo Hamalainen; Charles University, Czech Republic

Prof Abdollah Khodkar; University of West Georgia, USA

Dr Leonie Simpson; Queensland University of Technology

Professor J
ohn van Rees; The University of Manitoba

Prof Sule Yazici; Koc University, Turkey


Maenhaut

Dr. J. Egan; School of Mathematical Sciences, Monash University

Dr I M Wanless; School of Mathematical Sciences, Monash University

Dr B S Webb; Mathematics Depart
ment, Open University, United Kingdom

Dr D. J. Horsley; School of Mathematical Sciences, Monash University.


Street

Professor Chin
-
Mei Fu, Tamkang University, Tamsui, Taipei Shien, Taiwan

Professor Hung
-
Lin Fu, National Chiao
-
Tung University, Hsin
-
Chu, Tai
wan

Professor M J Grannell,Open University, Milton Keynes, United Kingdom

Professor T S Griggs, Open University, Milton Keynes, United Kingdom

Professor D G Hoffman, Department of Discrete and Statistical Sciences, Auburn University

Professor C C Lindner,
Department of Discrete and Statistical Sciences, Auburn University

Professor E S Mahmoodian, Department of Mathematical Sciences, Sharif University of

Technology, Tehran, Iran

Professor R Mathon, Department of Computer Science, University of Toronto

Profes
sor Jennifer Seberry, Department of Computer Science, University of Wollongong

Professor R G Stanton,

Department of Computer Science, The University of Manitoba

Professor Deborah J Street, Department of Mathematical Sciences, University of Technology,
Sydn
ey


Warnaar

A. Lascoux (CNRS),

R. Langer;
University of Melbourne

P.J. For
rester;
University of Melbourne

E. Rains (Caltech),

M. Schlosser (Vienna),

V.P. Spiridonov (Dubna),


Waterhouse

Dr Atif A. Abueida; University of Dayton, USA

Dr Nicholas Cavenagh
;

University of New South Wales

Dr Carlo Hamalainen; Charles University, Czech Republic

Prof Sule Yazici; Koc University, Turkey



11. H
ONOURS AND AWARDS


The Institute of Combinatorics and its Applications, an international body, was set up in 1990,
based

in Canada, with Professor W T Tutte as
P
resident and Professor R G Stanton as Registrar.
Street is one of the two Australians invited to become Founding Fellows of the ICA and served as
its President from1996
-
2002; Billington and Donovan are Foundation F
ellows; Adams
,
Bryan
t,
Maenhaut

and Gray are Fellows; Billington was on the ICA Council prior to 2001 and Donovan has
been on the ICA Council since 2006.


The ICA awards Kirkman Medals, recognising outstanding achievement by combinatorialists in the
earl
y stages of their careers; Adams, Bryant and Hamilton are Kirkman Medallists and in
2007
Bryant was awarded
at
2006 ICA Hall Medal.


Bryant has held a QEII Fellowship for the years 2002
--
2006

and 2007
-
2011.

Benjamin Burton, QEII Fellowship for the years 20
10
--
2015
.


12. THE CENTRE AND THE WIDER COMMUNITY

Staff associated with this Centre have been involved in the following outreach programs.


State, National and International Activities

Australian Mathematics Olympiad for Queensland students:

Scharaschkin i
s involved in the training
of students from Queensland for the AMO; this also includes the distribution and marking of
problems. (See http://www.maths.uq.edu.au/~victors/Olympiad/ .)


University and Cross
-
Faculty Activities

Enhanced Studies Program:
Billin
gton
co
-
ordinated the delivery of MATH1061 to Enhanced
Studies Students

in 2009
-
2010
. MATH1061 is an introductory discrete mathematics course which
exposes Year 12 students to both the theory and application of discrete mathematics.


EXPO Uni: Centre memb
ers have developed and staffed numerous exhibits which stress the
importance of discrete mathematics; for example, displays on secret key distribution schemes and
error detection techniques for barcodes.


Biological and Chemical Sciences Faculty Science Da
ys: Year 12 students attended special sessions
on campus.


Faculty Activities

School Liaison Program: A number of Centre staff and students have delivered talks on applications
of discrete mathematics and on career prospects to high school students.


Scho
ol of
Mathematics and Physics

Activities

Infinity: This wa
s a biennial newsletter which is produced by Billington, Donovan, and Maenhaut
with other members of this discipline, nam
ely, Cathy Holmes, Philip Isaac

and Michael Jennings.
Mailed to every high s
chool in Queensland, it provides a link between the University and the
broader community and has had great success in developing strong ongoing communications

between interested individuals and University staff.



13.

PUBLICATIONS AND WEB SITES


The names
of authors, associated with the Centre w
h
ile the work was carried out, appear in upper
case.


Journal edited
:

Australasian Journal of Combinatorics


20
09
-
10


BILLINGTON

E.J., Australasian Journal of Combinatorics
, Volumes 43, 44, 45 (2009); Volumes
46, 47
, 48 (2010).


Chapters in Books, 20
10


Refereed Journal Articles, 2010


ADAMS, P.,
Goos, M., and Matthew, K.,

Building the mathematical and computational skills of
science students,
Joint Mathematics Meetings, 2009


ADAMS
, P.,

Goos, M., and Matthew, K.,

Pu
tting it into perspective: Mathematics in the
undergraduate science curriculum
,
International Journal of Mathematics Education in Science and
Technology
,
2009
,

891


902


ADAMS, P.,
Goos, M., and Matthew, K.,

Putting it into perspective: Mathematics in the

undergraduate science curriculum,
7th Bi
-
annual Southern Right Delta Conference 2009


ADAMS, P.,
Eggleton, R. and MacDougall, J.,

Graphs which are linked cycles,
Congressus
Numerantium: A conference journal on numerical themes, 2009, 75
-

84


ADAMS, P.,
E
ggleton, R. and MacDougall, J.,

Graphs which are linked structures,
Congressus
Numerantium: a conference journal on numerical themes
,

2009
, 7
5


88


ADAMS, P.,

LEFEVRE, J.G., and WATERHOUSE M,

Some results on 2
-
perfect cube
decomposition,
Australasian Jour
nal of Combinatorics, 2009, 95


103


ADAMS, P.,
Ardal, H., Manuch, J. Hoa, V.D., Rosenfeld, M. and Stacho, L.,
Spanning cubic graph
designs,
Discrete Mathematics, 2009, 5781
-

5788


ADAMS, P.,

Gannaway, D., and Matthews, K.,

The impact of social learning
spaces on the student
experience,
Blended Learning Conference, 2009


ADAMS, P.,
Goos, M., and Matthew, K.,

Translating the principles of Bio2010 into practice
Joint
Mathematics Meetings, 2009


ADAMS, P
.,
Gannaway, D
., and Matthews, K.,

The impact of social

learning spaces on student
engagement,
Pacific Rim First Year in Higher Education Conference, 2009, 1
-

10


ADAMS, P., Gannaway, D. Matthews K.,

A model for driving large
-
scale quality learning in
higher education,
International Consortium for Educational

Development, 2010


ADAMS, P.,
BRYANT, D.E.,
Kulis, C., Long, S. Smythe, M., and Tran, T.,

Defining scaffold
geometries for interacting with proteins: Geometrical classification of secondary structure linking
regions
Journal of Computer
-
Aided Molecular
Design, 2010, 917


934


ADAMS, P.,
BILLINGTON, E.J., Hoffman, D.G. and Lindner, C.C.,

The generalized almost
resolvable cycle system problem,
Combinatorica

30(6)
,

2010, 617

625


ADAMS, P.,
Goos, M., and Matthew, K.,

Using the principles of Bio2010 to deve
lop an
introductory, interdisciplinary course for Biology students

CBE Life Sciences Education, 2010, 290


297


Alspach, B, and DEAN, M.,
Honeycomb toroidal graphs are Cayley Graphs
,

Information
Processing Letters, 109, no. 13, 2009, 705
-
708


Alspach,
B., Chen, C.C., DEAN M.,
Hamilton paths in Cayley graphs on generalized

dihedral
groups,
Ars Mathematica Contemporanea,
3, no. 1,

2010, 29

4
7


BILLINGTON, E.J.,
Kucukcifci, S., Lindner, C.C., and Yazici, E.S.,
Embedding 4
-
cycle systems
into

octagon triple systems
,
Utilitas Mathematica
,

79
(
2009
)
,
99
-
106


BILLINGTON, E.J.,

and Lindner, C.C.,
Embedding 5
-
cycle systems

into pentagon triple system
,
Discrete Mathematics
,

309(14)
,
2009
,

4828
-

4834



BI
LLINGTON, E.J.,

Cavenagh, N.J. and Smith, B.R.,

Path and cycle

decompositions of complete
equipartite
graphs: Four parts,
Discrete Mathematics
,

309(10)
,

(
2009
)
,

3061

3073
.


BILLINGTON, E.J. and LINDNER
, C.C., Embedding 5
-
cycle systems into pentagon triple systems,
Discrete Mathematics 309(14) (2009), 3061
-
3073.


BILLINGTON, E.J., Kucukcifci, S., Yazici, E.S. and LINDNER, C.C., Embedding 4
-
cycle systems
into octagon triple systems, Utilitas Mathematica 7
9 (2009), 99
-
106.


BILLINGTON, E.J.,
Cavenagh, N.J. and Smith, B.R.,

Path and cycle decompositions of complete
equipartite graphs: 3 and 5 parts
, 310(2),

(
2010
)
, 241

254
.


BRYANT, D.E.,
and
HORSLEY,

D.,

A proof of Lindner's conjecture on embeddings of par
tial
Steiner triple systems
, Journal of Combinatorial Designs, 17(1), 2009, 63
-

89



BRYANT, D.E
.,
and


SCHARASCHKIN, V.,
Complete solutions to the Oberwolfach problem for
an infinite set of orders,
Journal of Co
mbinatorial, Theory, Series B, 99
, 2009, 90
4
-

918


BRYANT, D.E.,
Completing partial commutative quasigroups constructed from partial Steiner
triple systems is NP
-
complete
,
Discrete Mathe
matics, 309(14),
2009,

4700
-

4704


BRYANT, D.E.,
Egan, J.,
MAENHAUT B. M,
and Wanless, I.M.,
Indivisible plexes

in latin
squares,

Designs, Codes and Cryptography, 2009, 52(1), 93
-

105


BRYANT, D.E.,
and BRIER, R.,
Perpendicular Rectangular Latin Arrays,
Graphs and
Combinatorics, 25(1), 2009, 15
-

25


BRYANT, D.E.,

and
MARTIN, G.,

Some results on decompositions of
low degree circulant graphs,

Australasian Journal of Combinatorics, 45(), 2009, 251
-

261



BRYANT, D.E.,
El
-
Zanati, S.I., Hartke, S.G., and Ostergard, P.R.J.,
The nonexistence of a (K6
-
e)
-
decomposition of the complete graph K29,

Journal of Combinatorial D
esigns, 18(2), 2009, 94
-

104


BRYANT, D.E.,

BUCHANAN, M., and Wanless, I.,
The spectrum for quasigroups with cyclic
automorphisms and additional symmetries,

Discrete Mathematics,


309(4), 2009,

821
-

833


BRYANT, D.E.,

and
HORSLEY,
, D,

Decompositions of c
omplete graphs into long

cycles
,

Bulletin
of the London Mathematical Society,

41(5),

2010,
927
-

934


BRYANT, D.E.,

Packing paths in complete graphs
,

Journal of

Combinatorial Theory, Series B
,

100(2),


2010,

206
-

215


BRYANT, D.E.,
and H

HORSLEY,
, D.,

An

asymptotic solution to the cycle decomposition
problem for complete graphs
, Journal of Combinatorial Theory Serie
s A, 117(8), 2010, 1258


1284


BURTON, B.A.,
Quadrilateral
-
octagon coordinates for almost normal surfaces
,
Experimental
Mathematicics 19:3
,
2
010
,
285

315


BURTON, B.A.,
Optimizing the double description method for normal surface enumeration

Mathematics of Computation 79
:269,
2010
,
453

484


BURTON, B.A.,
The complexity of the normal surface solution space
,
SCG ’10: Proceedings of
the Twenty
-
Sixt
h Annual Symposium on Comput
ational Geometry, ACM, 2010,

201

209


BURTON, B.A.,
Encouraging algorithmic thinking without a computer
,
Olympiads in Informatics
4
,

2010, 3

14


BURTON, B.A.,
Converting between quadrilateral and standard solution sets in normal

surface
theory

Algebraic & Geometric Topology 9
:4,
2009
,

2121

2174


DONOVAN, D.M.,
LEFEVRE, J.G., WATERHOUSE M. and Emine Sule

Yazizi,
On defining sets
of full

designs with block size three,

Graphs and Combinatorics, 25(6), 2009, 825
-

839



DONOVAN, D.M
., Grannell, M.J., Griggs, T.S. and LEFEVRE, J.G.,

On parity vectors of Latin
squares,

Graphs and Combinatorics,

26(5),

2010, 673
-

6842



DONOVAN, D.M., Drapal, A., Grannell, M.J., Griggs, T.S. and

LEFEVRE, J.G.,
Quarter
-
regular
biembeddings of Latin squa
res
,
Discrete Mathematics, 310(4),
2010, 692
-

699



DONOVAN, D.M., Grannell, M.J. and Griggs, T.S.

Third
-
regular

bi
-
embeddings of Latin squares
,
Glasgow Mathematical Journal, 52(3), 2010,

497
-

503



GRAY K.R. and STREET, A.P.,
On the number of mutually d
isjoint isomorphic (v, k, λ) designs,
Bulletin of the Institute of Combinatorics and its Applications, 60, 2010, 9
-

14





GRAY K.R. and STREET, A.P.,
Two regular solids holding the twelve (6, 3, 2) designs
, Bulletin of
the Institute of Combinatorics and
its Applications, 57, 2009, 53
-

59



GRAY K.R. and STREET, A.P.,
A method for constructing defining sets of all

(v, k,
\
lambda) designs
, Bulletin of the ICA, volume 59, May 2010, pages 71
-
82.



GRAY, K.R.,

STREET, A.P. and Stanton, R.G
., Using affine pla
nes to partition full designs with
block size three
, Ars Combinatoria, XCVIIA, 2010, 383
-

402




Langer, R., Schlosser, M.J. and
WARNAAR, S.O.,
Theta functions, elliptic hypergeometric series,
and Kawanaka's Macdonald polynomial conjecture,

Workshop on El
liptic Integrable Systems,
Isomonodromy Problems, and Hypergeometric Functions, 5, 2009, 055:1
-

055:20


Lascoux, A., Rains, E., and
WARNAAR, S.O.,

Nonsymmetric interpolation Macdonald
polynomials and gln basic hypergeometric series Transformation groups
,

14(3),

2009,

613


647


LEFEVRE, J.G. DONOVAN, D.M., Grannell, M.J. and Griggs, T.S.,

A constraint on the
biembedding of Latin squares
, European Journal of Combinatorics, 30(2), 2009, 380


386


McCOURT, T.A.
The intersection problem for disjoint

2
-
flowe
rs in Steiner triple systems,
Journal of
Combinatorial Mathematics and Combinatorial Computing, 75, 2010, 41


63


McCOOURT, T.A.
On defining sets in latin squares and two intersection problems, one for latin
squares and one for Steiner triple systems,

Bull
etin of the Australian Mathematical Society, 82(2),
2010, 351


352


Polh
, W., BURTON, B.A., D
agiene
, V., F
akchoenphol
, J., F
orisek
, M., H
iron
, H., O
pmanis
, M.,
S
kupas
, B., V
an

D
er

V
egt
, W.,
Get involved! The IOI workshop 2010, its goals and results
,
Oly
mp
iads in Informatics 4,
2010
,

158

169



Rao, A., DONOVAN, D.M., and Hall, J.L.,
Mutually orthogonal

Latin squares and mutually
unbiased bases in dimensions of odd

prime power MOLS and MUB
s in odd prime power
dimensions,
Cryptography and Communications, 2(2)
, 2010, 221
-
231.


STREET, A.P. and
Nester M.R.
,
An introduction to

balanced sequen
tial arrays on the square grid,

Mathematica

Slovaca
, 59(2), 2009, 177


192


WARNAAR, S.O.,
A Selberg integral for the Lie algebra,
Acta Mathematica,
203(2), 2009, 269
-

304



WARNAAR, S.O.,
The sl(3) Selberg integral,

Advances in Mathematics,
224(2), 2010, 499
-

524


Forrester, P. J. and WARNAAR, S. O.
The importance of the Selberg integral
. Bulletin of the
American Mathematical Society,
45 04:

(2008)
489
-
534.