Combinatorics Research Group
Research in combinatorics covers a wide range of topics in graph theory, matroid theory, orthogonal polynomials and random matrices. For detailed descriptions of our research as well as other relevant information (collaborations, lists of publications, projects) please follow the links to the web pages of individual group members.
Recent research includes:- Investigating graph polynomials such as the Tutte polynomial, in particular their complexity.
- Researching into polynomial inequalities and non-asymptotic bounds for orthogonal polynomials.
- Establishing new strengthenings of 3-connectivity in matroids as a tool to prove chain-type or splitter-type theorems.
- Calculating asymptotics of orthogonal polynomials and asymptotics of related Toeplitz, Hankel and Fredholm determinants.
- Investigating the frequency assignment and related graph colouring / labelling problems, for example, determining the complexity of the L(2,1) labelling problem for outerplanar and planar graphs.
- Establishing new bounds for the 3x+1 problem.
There is active international collaboration with New York University, University of Waterloo, Universidad Nacional Autonoma of Mexico, Louisiana State University, Victoria University of Wellington and Indiana University - Purdue University. Members of the combinatorics group form part of BURSt and the Brunel Complexity Community
Current Research and Teaching Networks:
- European Early-stage Training Site NET-ACE
- Brunel Complexity Community
- London Taught Course Centre LTCC
