Combinatorics, Special Functions, and Computer Algebra

组合学、特殊函数和计算机代数

• 批准号: 9500646
• 负责人: Doron Zeilberger
• 金额: $ 12万
• 依托单位: Temple University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500646&HistoricalAwards=false
• 关键词: Combinatorics; Special; Functions; Computer; Algebra

This award supports the research of Professor Doron Zeilberger in the areas of algebraic combinatorics, the theory of special functions, and computer algebra. One direction of this project is a continuation of his research program on the use of computer algebra for computerized proofs of identities in combinatorics and the theory of special functions. Other goals of this project include the development of a general theory of permutation statistics, the study of holonomic aspects of combinatorial statistical mechanics, and the extension of methods developed in the principal investigator's recent proof of the alternating sign matrix conjecture to other, still open, problems in this area. Because both special functions and combinatorics are so prevalent in the natural sciences, this research has many potential applications to both science and technology, as well as to pure mathematics. 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 large 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 Doron Zeilberger 教授在代数组合学、特殊函数理论和计算机代数领域的研究。该项目的方向之一是他的研究计划的延续，即使用计算机代数进行组合数学和特殊函数理论中恒等式的计算机化证明。该项目的其他目标包括发展排列统计的一般理论，研究组合统计力学的完整方面，以及将主要研究者最近证明交替符号矩阵猜想中开发的方法扩展到该领域其他尚未解决的问题。 由于特殊函数和组合数学在自然科学中非常普遍，因此这项研究在科学技术以及纯数学方面都有许多潜在的应用。 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，大型网络的设计（例如电话系统中的网络）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。