Classical Combinatorics: An International Conference

由Dominique Foata提出的“经典组合学”一词，大致是“经典分析”的组合类比。今天，它更为人所知的是枚举法和代数组合学。作为现代数学发展最快的领域之一，它涉及到数学和科学的许多领域，也构成了计算机科学的基础之一。本次会议将侧重于列举组合学的更经典的方面，如排列统计、表象、Q级数、字、组合特殊函数论、交换么半群和相关学科，以及它们与计算机科学、物理和统计学的关系。经典组合学被应用于算法理论中，其中排列和表形成了排序和搜索的理论基础，在并行编程理论、统计物理和许多其他地方。仅举一个最近的例子，Bass对图的Ihara Zeta函数求值的Foata-Zeilberger扩展被林和王用于纽结理论，获得了极大的优势。研究人员和他们的同事研究古典组合学的各个方面，并将会议作为这一领域新研究激增的关键工具。组合学的目标之一是找到有效的方法来研究如何安排离散的对象集合。离散系统的行为对于现代通信来说是极其重要的。例如，大型网络的设计，如那些发生在电话系统中的网络，以及计算机科学中的算法设计，都涉及离散的对象集，这利用了组合研究。这次会议将汇聚该领域的领导者和新兴的研究人员，讨论组合数学领域的新想法。

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.