The Structure of Permutation Classes

排列类的结构

• 批准号: 1301692
• 负责人: Vincent Vatter
• 金额: $ 16万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1301692&HistoricalAwards=false
• 关键词: Structure; Permutation; Classes

The overarching aim of this project is to expand the structural theory of permutation classes, to unify the disparate strands coming together in this theory, and to test the power of the emerging viewpoint and toolbox by bringing them to bear on problems of exact enumeration and the characterization of growth rates.Historically, the study of permutation classes arose from two independent streams in 1960s and 1970s. One was combinatorial in nature, and concentrated on the enumeration problems for permutations with a small set (size 1 or 2, typically) of short (length up to 4) forbidden patterns. The other was coming from Theoretical Computer Science, and was concerned with sets arising from common sorting mechanisms and their combinations. In the past 10 years or so these two strands have come much closer together, and this interaction has created a new, fast developing area of combinatorics, with significant interactions with Theoretical Computer Science, the Theory of Computability and Complexity, Algebra, and Computational Biology, to name only a few. Apart from the continued interest in sorting mechanisms and enumeration problems, major new strands of research have emerged including the structural theory of classes, the asymptotic behavior of classes, generalized pattern avoidance, packing densities, algorithmic and decidability problems, and geometrical methods.

该项目的总体目标是扩展排列类的结构理论，统一该理论中的不同分支，并通过将新兴观点和工具箱应用于精确枚举和排列问题来测试新兴观点和工具箱的力量。增长率的表征。从历史上看，排列类的研究起源于 20 世纪 60 年代和 1970 年代的两个独立流派。其中一个本质上是组合问题，集中于一小组（通常为 1 或 2）短（长度最多 4 个）禁止模式的排列的枚举问题。另一个来自理论计算机科学，关注由常见排序机制及其组合产生的集合。在过去十年左右的时间里，这两条线索更加紧密地结合在一起，这种相互作用创造了一个新的、快速发展的组合数学领域，与理论计算机科学、可计算性和复杂性理论、代数和计算生物学具有重要的相互作用，仅举几例。除了对排序机制和枚举问题的持续兴趣之外，还出现了主要的新研究领域，包括类的结构理论、类的渐近行为、广义模式避免、包装密度、算法和可判定性问题以及几何方法。