EAPSI: Analyzing Patterns in Permutations

排列是一种数学模型，可以用来表示一系列数据，就像计算机算法和股市趋势中的数据一样。通过仔细研究排列中各种模式的频率，人们可以发现对数据集本身的更好理解。这个项目将研究一类特殊的排列，这种排列起源于计算机科学中的分类机器领域。这项研究将与墨尔本大学澳大利亚研究委员会复杂系统数学和统计卓越中心的安东尼·古特曼教授共同进行。研究人员将把古特曼最初开发的技术用于研究数学物理中的相变和临界现象，并将其应用于排列模式领域。这个项目的主要目标是对一些特定置换类的渐近性质进行分类，这些置换类被猜想表现得不同于以前研究的任何置换类。此外，研究人员将利用古特曼的计算资源来寻找其他可能表现出同样奇怪性质的排列类别。这项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提供资金。

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.