Algebra, Combinatorics & Number Theory

The main acitivites of this group form part of the Centre for Discrete Mathematics and Computing which was established in 1998. The aim of this centre is to carry out and promote research and teaching in discrete mathematics and computing, and to facilitate collaborative research with groups working in related areas in Australia and overseas. The Centre acts as regional base for the Combinatorial Mathematics Society of Australasia and publishes the Australasian Journal of Combinatorics. It also acts as a national base for an international body, the Institute of Combinatorics and its Applications. The Number Theory Web is adminstered by Keith Matthews.

For more information follow the links to people's personal web pages.

Peter Adams

Combinatorial computing, graph decompositions, latin squares and critical sets, drug design, DNA sequencing.

Elizabeth Billington

Graph decompositions, trades in graphs and designs and their applications.

Darryn Bryant

Graph decompositions and colouring, steiner triple systems, Latin squares and perfect factorisations, combinatorial genome analysis.

 

Diane Donovan

Latin squares and critical sets, defining sets, trades in latin squares, combinatorial applications particularly to information security.

 

Ken Gray

 

James Lefevre

Barbara Maenhaut

Combinatorial design theory, graph theory.

Victor Scharaschkin

Number theory, cryptology.

Anne Street

Defining sets, trades in designs, combinatorial applications.

 

Mary Waterhouse

Current Students

  • Jenna Appleton, Aspects of computational combinatorial graph theory. Advisors: Peter Adams, Darryn Bryant.
  • Robert Brier, Topics in graph decomposition and related algebras. Advisors: Darryn Bryant, Barbara Maenhaut.
  • Melinda Buchanan, Problems on the existence and embedding of  Latin squares. Advisors: Darryn Bryant, Peter Adams.
  • Matthew Dean, On Hamilton cycles and Hamilton cycle decompositions of graphs based on groups. Advisors: Darryn Bryant, Peter Adams.
  • Tristan Freiberg, Chabauty methods. Advisors: Victor Scharaschkin, Keith Matthews.
  • Carlo Hamalainen, Critical sets for latin squares and graph colourings. Advisors: Diane Donovan, Elizabeth Billington, Nicholas Cavenagh.
  • Daniel Horsley, Topics in Steiner triple systems and related combinatorial designs. Advisors: Darryn Bryant, Barbara Maenhaut.
  • Thomas McCourt, Advisors: Diane Donovan, James Lefevre, Elizabeth Billington.
  • Trevor Pickett, An investigation of combinatorial configurations and their substructures. Advisors: Diane Donovan, Peter Adams.
  • Benjamin Smith, Graphs: decompositions and dynamic changes. Advisors: Elizabeth Billington, Barry Jones.