EPSRC grant success for Robert Brignall

Friday, Feb 24th 2012

Robert Brignall has been awarded a £114k grant from EPSRC under their 'First Grant' scheme for a one-year proposal entitled 'Infinite Antichains of Combinatorial Structures.'

Some of the most celebrated results in combinatorics of the last 50 years concern the study of well-quasi-ordering of combinatorial structures, i.e. the existence, or otherwise, of infinite antichains for objects such as graphs, tournaments or permutations under various natural orderings. In certain cases no infinite antichains exist (for example graphs under the minor ordering), but in others they do exist, and for some structures they appear in abundance.

Recent research by Robert has developed a general construction for infinite antichains of permutations. This construction not only adds to the body of evidence that the so-called 'fundamental' antichains have a much more regular structure than is guaranteed by their definition, but also suggest a hypothesis about the nature of this regularity. The proposal, which includes funding for a one-year postdoctoral research assistant, will extend this construction to other combinatorial structures, and thus provide evidence for or against the structural hypothesis.


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