Dr Robert Brignall

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. Recent research by the PI has developed a general construction for infinite antichains for permutations, which in turn gives a technique that can be used more generally for other structures. These constructions not only add evidence to the widely-held belief that the only infinite antichains that need to be considered in the study of well-quasi-ordering have a “regular” structure, but also suggest what this regular structure might be. This proposal aims to investigate this structure further, by first considering further examples in the study of permutation patterns, with particular reference to “grid classes”. It is hoped that the insight gained by studying examples in permutations will lead to more general structural results for antichains in other structures, and also explain the differences between the various structures.

LMS Research Scheme Grant - Grant reference: 11579 - Title of Conference: Mathematics in the regions: Staff Tutor Research Grant for Conference to be held in October 2016