Classical Combinatorics: An International Conference

经典组合学：国际会议

• 批准号: 9985949
• 负责人: Doron Zeilberger
• 金额: $ 1万
• 依托单位: Temple University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-07-01 至 2000-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9985949&HistoricalAwards=false
• 关键词: Classical; Combinatorics; International; Conference

AbstractThe term `Classical Combinatorics,' coined by Dominique Foata, is roughly the combinatorial analog of `Classical Analysis'. Today it is better known as enumerative and algebraic combinatorics. One of the fastest-growing areas of modern mathematics, it touches upon many areas of mathematics and science, as well as forming one of the foundations of computer science. This conference will emphasize the more classical aspects of enumerative combinatorics, like permutation statistics, tableaux, q-series, words, combinatorial special function theory, commutation monoids, and related subjects, as well as their relation to computer science, physics, and statistics. Classical Combinatorics is applied in the theory of algorithms, where permutations and tableaux form the theoretical foundation for Sorting and Searching, in the theory of parallel programming, statistical physics, and many other places. To cite just one very recent example, the Foata-Zeilberger extension of Bass's evaluation of the Ihara Zeta function of a graph was used in knot theory, by Lin and Wang, to great advantage. The investigators and their colleagues study various aspects of Classical Combinatorics and use conferences as a key tool in the proliferation of new research in this area.One of the goals of Combinatorics is to find efficient methods of studying how discrete collections of objects can be arranged. The behavoir 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. This conference will bring together leaders in the field and emerging researchers to discuss new ideas in the field of Combinatorics.

由Dominique Foata创造的“经典组合学”一词，大致上是“经典分析”的组合类比。 今天，它是更好地称为枚举和代数组合。 它是现代数学发展最快的领域之一，涉及数学和科学的许多领域，也是计算机科学的基础之一。 本次会议将强调枚举组合学的更经典的方面，如置换统计，tableaux，q系列，单词，组合特殊函数理论，交换monoid和相关主题，以及它们与计算机科学，物理学和统计学的关系。 经典组合学应用于算法理论、并行编程理论、统计物理学和许多其他地方，其中排列和表格构成了排序和搜索的理论基础。 仅举一个最近的例子，巴斯对图的伊原泽塔函数的评价的Foata-Zeilberger扩展被林和王用于纽结理论，具有很大的优势。 研究人员和他们的同事们研究经典组合学的各个方面，并将会议作为这一领域新研究扩散的关键工具。组合学的目标之一是找到研究如何安排离散对象集合的有效方法。 离散系统的解调对于现代通信是极其重要的。 例如，大型网络的设计，如电话系统中的网络设计，以及计算机科学中的算法设计，都要处理离散的对象集，这就需要使用组合研究。 本次会议将汇集该领域的领导者和新兴研究人员，讨论组合数学领域的新思想。