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 40 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