Permutation Patterns 2011

排列模式 2011

• 批准号: 1105569
• 负责人: Anthony Mendes
• 金额: $ 2万
• 依托单位: California Polytechnic State University Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-02-15 至 2013-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1105569&HistoricalAwards=false
• 关键词: Permutation; Patterns; 2011

This grant supports a conference on Permutation Patterns in the Summer of 2011 at the California Polytechnic State University in San Luis Obispo, California. As in past conferences, we expect to attract many graduate students and junior researchers. In total, we expect around 70 participants and around 35 talks. The topic of the conference is permutation patterns and, more generally, the concept of pattern in mathematical objects such as partitions, words, and other structures such as genome sequences. A permutation of length n is a rearrangement of the integers 1 through n. If a permutation sigma can be found by erasing some of the integers in a permutation tau and renumbering the remaining integers in sequential order with 1 through k, then we say that sigma is involved in tau. The study of permutation patterns is concerned with understanding this involvement relation.The definition of involvement can be rephrased in a variety of contexts such as geometric or model-theoretic. In computer science, sets of permutations which are closed under involvement are found in the study of sorting devices such as stacks, queues, and finite networks. The past decade or so has seen a confluence of ideas stemming from combinatorics and the computer science, creating new and developing avenues of research in mathematics, theoretical computer science, computability and complexity theory, and computational algebra. In addition to the continuing interest in the combinatorics and sorting mechanism problems, some major new directions include the structural theory of permutation patterns (constructions, decompositions, etc.), asymptotics, variations and generalizations such as the concept of generalized pattern avoidance, packing densities, algorithmic and decidability problems, and geometrical methods.The study of permutation patterns has emerged as a significant branch of enumerative combinatorics over the past couple of decades. Hundreds of papers on permutation patterns have appeared relatively recently. The number of researchers in the area is increasing and the attendance in the annual conference on permutation patterns has steadily grown since its inception in 2003. Research is international across North America, Europe, Asia, and Australasia. This is a subject of global interest.The subject of permutation patterns has a relatively low mathematical overhead. Some of the commonly used tools used to investigate permutation patterns include generating functions, algorithm design, experimental computation; tools which permeate combinatorics and computer science. Therefore, this subject is accessible to entry-level researchers. Our conference will provide opportunities for young researchers to learn about and begin to make contributions to the theory. The number of graduate students who have attended the last two meetings is an indication that research in this subject area is growing.

这项拨款支持2011年夏天在加州圣路易斯奥比斯波的加州州立大学举行的排列模式会议。 与过去的会议一样，我们希望吸引许多研究生和初级研究人员。 我们预计总共有大约70名与会者和大约35场会谈。 会议的主题是排列模式，更普遍的是数学对象中的模式概念，如分区，单词和其他结构，如基因组序列。 长度为n的置换是整数1到n的重新排列。 如果可以通过擦除置换tau中的一些整数并将剩余的整数按1到k的顺序重新编号来找到置换sigma，则我们说sigma涉及tau。 置换模式的研究关注于理解这种涉入关系，涉入的定义可以在各种背景下重新表述，如几何或模型论。 在计算机科学中，在参与下闭合的排列集合在对诸如堆栈、队列和有限网络之类的排序设备的研究中被发现。在过去的十年左右，组合数学和计算机科学的思想融合在一起，创造了数学、理论计算机科学、可计算性和复杂性理论以及计算代数的新的和发展中的研究途径。 除了对组合学和排序机制问题的持续兴趣之外，一些主要的新方向包括排列模式的结构理论（构造，分解等），置换模式的研究在过去的几十年里已经成为计数组合学的一个重要分支。 最近出现了数百篇关于排列模式的论文。 该领域的研究人员数量正在增加，自2003年成立以来，每年的排列模式会议的出席人数稳步增长。 研究是国际性的，横跨北美，欧洲，亚洲和澳大拉西亚。 这是一个全球感兴趣的主题。置换模式的主题具有相对较低的数学开销。 一些用于研究置换模式的常用工具包括生成函数，算法设计，实验计算;渗透组合学和计算机科学的工具。 因此，这个主题是入门级研究人员可以访问的。 我们的会议将为年轻的研究人员提供机会，了解和开始作出贡献的理论。 参加前两次会议的研究生人数表明，这一主题领域的研究正在增长。