Conference on Permutation Patterns 2010

2010 年排列模式会议

• 批准号: 1003908
• 负责人: Sergi Elizalde
• 金额: $ 1.45万
• 依托单位: Dartmouth College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-03-15 至 2011-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1003908&HistoricalAwards=false
• 关键词: Conference; Permutation; Patterns; 2010

This conference is devoted to permutation patterns, i.e., the study of permutations with respect to the involvement order. A pattern in a permutation written in one-line notation is a subsequence whose entries have a prescribed relative order. This definition can be re-phrased in various different contexts, e.g. geometrical, where a permutation is identified with its plot, and model-theoretic, where a permutation is taken to be a set with two linear orders defined on it. Of particular interest are the sets of permutations which are closed under involvement. These are precisely the sets of permutations which can be defined by avoiding (i.e. not involving) prescribed sets of permutations ("forbidden patterns"). The conference topics include enumeration questions, algorithmic problems, and applications and generalizations of permutation patterns.Historically, the study of pattern containment in permutations 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.

本次会议的主题是排列模式，即研究与介入顺序相关的排列。用单行表示法编写的排列中的模式是子序列，其项具有规定的相对顺序。这个定义可以在各种不同的背景下重新表述，例如，几何上，一个排列被识别为它的图，而模型理论上，一个排列被认为是在它上面定义了两个线性顺序的集合。特别令人感兴趣的是在卷入下闭合的置换集。这些恰恰是可以通过避免（即不涉及）规定的排列集（“禁止模式”）来定义的排列集。会议主题包括枚举问题、算法问题以及排列模式的应用和概括。历史上，排列中的模式包容研究起源于20世纪60年代和70年代两个独立的流派。一个本质上是组合的，专注于短（长度最多为4）禁止模式的小集合（通常为1或2）的排列枚举问题。另一个来自理论计算机科学，关注的是由普通排序机制和它们的组合产生的集合。在过去10年左右的时间里，这两条线走得更近了，这种相互作用创造了一个新的、快速发展的组合学领域，与理论计算机科学、可计算性和复杂性理论、代数和计算生物学等有重要的相互作用。除了对排序机制和枚举问题的持续兴趣外，还出现了主要的新研究方向，包括类的结构理论、类的渐近行为、广义模式回避、填充密度、算法和可判定性问题以及几何方法。