Infinite antichains in small permutation classes

有关模式避免置换类的一般背景，请参阅Vatter最近的调查。在置换类的研究中，Marcus和Tardos的一个著名结果断言VCN中的limsupn由一个常数有界，其中Cn表示给定类中长度为n的置换的个数。最小的上界是增长率的上界，一般情况下，nVCN是否有一个真正的极限(这类增长率)仍然是一个悬而未决的问题。在两篇重要的论文中，Vatter2和3对低于2.30522的置换类的所有可能的增长率进行了分类。这项研究的核心是，在一些置换类中出现了无限的反链，这引发了相当大的麻烦。这个PHD建议涉及良好的准有序置换类，即那些在增长率4以下的范围内不包含无限反链的置换类。

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.