Mathematical Sciences: Algebraic Shifting

数学科学：代数平移

• 批准号: 9510655
• 负责人: Helene Barcelo
• 金额: $ 1.8万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-15 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9510655&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Shifting

This award supports the research of Professor Helene Barcelo in the field of algebraic combinatorics. The algebraic shifting method introduced by Kalai in 1984 has proven to be an extremely successful tool for characterizing the f-vectors of a wide range of classes of simplicial complexes. The goal of this research is to investigate possible generalizations of this method to algebraic structures other than simplicial complexes. The algebraic structures to be studied share the common property that they have a class of combinatorial objects associated with them. This research is in the general area of Combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections of objects can be arranged. The behavior of discrete systems is extremely important to modern communications. For example, the design of lapge networks, such as those occurring in telephone systems, and the design of algorithms in computer science deal with discrete sets of objects, and this makes use of combinatorial research.

该奖项支持 Helene Barcelo 教授在代数组合领域的研究。 Kalai 于 1984 年引入的代数平移方法已被证明是一种极其成功的工具，用于表征各种单纯复形的 f 向量。本研究的目的是研究该方法对单纯复形以外的代数结构的可能推广。要研究的代数结构具有共同的属性，即它们具有与之相关的一类组合对象。 这项研究属于组合学的一般领域。组合学试图找到有效的方法来研究如何排列离散的对象集合。离散系统的行为对于现代通信极其重要。例如，电话系统中出现的重叠网络的设计，以及计算机科学中处理离散对象集的算法设计，都利用了组合研究。