Enumerative Problems Concerning Oriented Matroids

有关有向拟阵的枚举问题

• 批准号: 0101209
• 负责人: James Lawrence
• 金额: --
• 依托单位: George Mason University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-15 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0101209&HistoricalAwards=false
• 关键词: Enumerative; Problems; Concerning; Oriented; Matroids

An oriented matroid is a combinatorial abstraction which can be used to encapsulate features of a nite point set in Euclidean space which are of interest in combinatorial geometry. It is planned to study certain enumeration problems involving oriented matroids by making use of the theory of valuations on distributive lattices. Indeed some progress along these lines has already been made. It is hoped that information on the range of certain important functions for example, the f-vectors of convex polytopes, or the number of "k-sets" of a finite point set will be generated. Additionally it is hoped that this research will enable the extension to oriented matroids in general of substantial results already obtained for uniform oriented matroids.Combinatorial geometry is a subject with a venerable history which in recent years has become an even more important arena for research, due to its applications in the area of algorithms for geometrical structures. Research in combinatorial geometry often leads to better algorithms in computational geometry, which in turn leads, for example, to improved design of computer chips, better algorithms for image analysis and processing, and so forth.

定向拟阵是一种组合抽象，它可以用来封装欧氏空间中nite点集的特征，这些特征是组合几何中感兴趣的。利用分配格上的赋值理论，研究某些涉及定向拟阵的计数问题。事实上，在这些方面已经取得了一些进展。希望能产生关于某些重要函数的范围的信息，例如凸多面体的f-向量，或有限点集的“k-集”的数目。组合几何是一门历史悠久的学科，近年来由于其在几何结构算法领域的应用而成为一个更加重要的研究领域。组合几何的研究往往导致计算几何中更好的算法，这反过来又导致例如，计算机芯片的改进设计，图像分析和处理的更好的算法，等等。