Infinite antichains in small permutation classes

小排列类中的无限反链

• 批准号: 2448505
• 金额: --
• 依托单位: The Open University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2448505
• 关键词: Infinite; antichains; small; permutation; classes

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.

有关避免置换类别的模式的一般背景，请参见Vatter的最新调查。在对置换类别的研究中，由于Marcus和Tardos引起的著名结果断言VCN中的Limsupn受常数的界定，其中CN表示给定类别中长度N的排列数。最小的上限是上层的速率，总体上，N VCN是否具有真正的限制（班级的增长速度（班级的增长率）。在两篇重要的论文中。在两篇重要的论文中，Vatter 2和3归类了所有可能的置换类别的增长速度以下= 2.30522 = 2.30522。对于研究的核心，对研究的核心，并且在某些允许的类别中造成了一些允许的限制。在低于生长速率的范围内包含无限的抗细胞4。