Infinite antichains in small permutation classes

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For a general background to pattern avoiding permutation classes, see Vatter's recent survey. In the study of permutation classes, a famous result due to Marcus and Tardos asserts that limsupn in vcn is bounded by a constant, where cn denotes the number of permutations of lengths n in a given class. The smallest upper bound is the upper grown rate, and it remains an open problem in general whether n vcn has a true limit (th growth rate of the class. In two important papers, Vatter 2 and 3 classifies all possible growth rates of permutation classes below = 2.30522. Central to the study, and causing considerable trouble, is the appearance of infinite antichains inside some permutation classes. This PhD proposal concerns well quasi ordered permutation classes i.e. those that do not contain infinite antichains in the range below growth rate 4.