Classical Combinatorics: An International Conference

摘要“古典组合学”一词是多米尼克·福阿塔（Dominique Foata）创造的，大致相当于“古典分析”的组合类比。今天，它被称为枚举和代数组合学。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经典方面，如置换统计、表型、q级数、词、组合特殊函数理论、对易单群和相关学科，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，其中排列和表形构成了排序和搜索的理论基础，应用于并行编程理论、统计物理和许多其他领域。举一个最近的例子，Foata-Zeilberger扩展了Bass对图的Ihara Zeta函数的评价，Lin和Wang在结理论中使用了Foata-Zeilberger扩展，得到了很大的好处。研究者和他们的同事研究经典组合学的各个方面，并将会议作为该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离散对象集合如何排列的有效方法。离散系统的行为对现代通信极为重要。例如，大型网络的设计，比如那些出现在电话系统中的网络，以及计算机科学中处理离散对象集的算法设计，这就利用了组合研究。本次会议将汇集该领域的领导者和新兴研究人员来讨论组合学领域的新思想。

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.