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Mike Grannell

Research


Combinatorics Research Group (CRG)

The Open University has a large and active research programme in combinatorics. Combinatorics is a rich source of mathematical questions which are easily described but difficult to solve. The CRG's current investigations focus on graph colourings, combinatorial designs and their properties, topological embeddings of graphs and designs, and pattern-avoiding permutations. Fuller details may be found by following this link. Our interest is primarily and unashamedly in the theoretical aspects. However, many of the questions connect with practical issues in areas such as experimental design, data transmission, and data security. A specific example is the application of graph colourings to mobile telephone transmission systems. The questions which we seek to address are recognised as significant both for their theoretical importance and for their practical implications.

My research

Most of my research over the past 30 years has been done jointly with my colleague Terry Griggs. Our interests are focused on Steiner triple systems, their properties and those of related combinatorial designs. We have several papers on configurations in Steiner triple systems and other designs.  Since the mid-1990s we have developed an interest in topological representations of designs and from 2002 - 2006 we held a Leverhulme Trust grant to pursue this topic with colleagues at the Slovak University of Technology.

For anyone wishing to study combinatorial designs, a good general introduction may be found in:
I. Anderson. A first course in combinatorial mathematics (second edition), Oxford University Press, 1989.

Research aspects are dealt with more fully in:
C. J. Colbourn and A. Rosa, Triple systems, Oxford University Press, 1999.

A survey of work in topological design theory is given in:
Designs and topology. (M. J. Grannell and T. S. Griggs.) Invited paper for the 2007 British Combinatorial Conference, in "Surveys in Combinatorics 2007", Cambridge University Press, London Mathematical Society Lecture Note Series 346 (ISBN13: 9780521698238), 2007, 121-174.

For a full list of my publications, go to My papers

Contact: Mike Grannell mike.grannell@open.ac.uk