EAPSI: Analyzing Patterns in Permutations

EAPSI：分析排列模式

• 批准号: 1514825
• 负责人: Jay Pantone
• 金额: $ 0.51万
• 依托单位: Pantone Jay
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-06-01 至 2016-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1514825&HistoricalAwards=false
• 关键词: EAPSI; Analyzing; Patterns; Permutations

Permutations are a mathematical model that can be used to represent series of data like those found in computer algorithms and stock market trends. By carefully studying the frequency of various patterns in permutations, one can find a greater understanding of the data set itself. This project will investigate a special class of permutations that originates via the field of sorting machines in computer science. The research will be conducted with Professor Anthony Guttmann at the Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems at the University of Melbourne.The researcher will apply the techniques originally developed by Guttmann for the study of phase transitions and critical phenomena in mathematical physics to the field of permutation patterns. The main goal of this project is to classify the asymptotic nature of a number of specific permutation classes that are conjectured to behave unlike any permutation class studied before. Furthermore, the researcher will utilize the computational resources of Guttmann to search for other permutation classes that may exhibit the same strange properties.This NSF EAPSI award supports the research of a U.S. graduate student and is funded in collaboration with the Australian Academy of Science.

排列是一种数学模型，可用于表示计算机算法和股票市场趋势中发现的一系列数据。通过仔细研究排列中各种模式的频率，人们可以更好地理解数据集本身。这个项目将研究一类特殊的排列，它起源于计算机科学中的排序机领域。研究人员将与墨尔本大学澳大利亚研究理事会复杂系统数学和统计卓越中心的Anthony Guttmann教授合作，将Guttmann最初为研究数学物理中的相变和临界现象而开发的技术应用于排列模式领域。这个项目的主要目标是对一些特定的置换类的渐近性质进行分类，这些置换类的行为与以前研究的任何置换类都不同。此外，研究人员将利用古特曼的计算资源来搜索可能表现出相同奇怪性质的其他置换类。这个NSF EAPSI奖支持一名美国研究生的研究，并与澳大利亚科学院合作资助。