Conference on Permutation Patterns 2010

本次会议致力于排列模式，即，关于参与顺序的排列的研究。用单行符号表示的排列中的模式是一个子序列，其条目具有规定的相对顺序。这个定义可以在各种不同的上下文中重新表述，例如几何的，其中置换用它的图来标识，以及模型理论的，其中置换被认为是具有两个线性阶的集合。特别感兴趣的是在参与下闭合的置换集合。 这些正是可以通过避免（即不涉及）指定的排列集合（“禁止模式”）来定义的排列集合。会议主题包括枚举问题、算法问题以及置换模式的应用和推广。历史上，置换中的模式包含研究起源于20世纪60年代和70年代的两个独立的潮流。一个是组合的性质，并集中在枚举问题的排列与一个小的集合（大小1或2，通常）的短（长度高达4）禁止模式。另一个来自理论计算机科学，关注的是常见排序机制及其组合产生的集合。在过去的10年左右，这两条链已经走得更近了，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，代数和计算生物学有着重要的相互作用，仅举几例。 除了继续感兴趣的排序机制和枚举问题，主要的新的研究领域已经出现，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，和几何方法。

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.